unsmoothing real estate returns: a regime switching approach
DESCRIPTION
Unsmoothing Real Estate Returns: A Regime Switching Approach. Colin Lizieri, Stephen Satchell and Warapong Wonwachara Department of Land Economy / Department of Economics University of Cambridge. European Real Estate Society Conference Milano May 2010. Not Another Paper on Smoothing?. - PowerPoint PPT PresentationTRANSCRIPT
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Unsmoothing Real Estate Returns:A Regime Switching Approach
Colin Lizieri, Stephen Satchell and Warapong Wonwachara
Department of Land Economy / Department of EconomicsUniversity of CambridgeEuropean Real Estate Society ConferenceMilano May 2010
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Not Another Paper on Smoothing? Many studies analysing impact of appraisal process on valuation-based real estate indicesStandard method assumes time-invariant process
Can we maintain this assumption?Transaction-based indices and adjustment for liquidityTail dependence and behaviour in bubbles / crashesIntuition here: may be a regime-based structureFor returns process (Lizieri et al., Brooks & Maitland-Smith)For smoothing process (Chaplin, informal model)
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The Index Issue FT Returns m 2.02% s 8.58% rt,t-1 0.014IPD Returnsm 2.15% s 3.25% rt,t-1 0.813
Chart1
2.443667650218.841917038
2.72494815.2607927322
4.9526476865.616584
5.6194024086-32.0026550293
5.19769763954.0549674034
8.0297268.310058
7.261537-0.4158257
6.685861-1.0190192461
4.790126323715.8391513824
5.1729773.7536697388
4.20709753047.152185
1.28220224384.0634436607
-0.08922204-6.530186
-2.35553145416.268623
-2.1429033279-18.13032341
-2.02860856068.147772
-1.675187230115.4552135468
-0.08520085-1.2575266361
-0.0498918310.16984272
1.0617476702-5.514645
0.2975316346-0.1393856108
0.38536563525.096318
-0.81754880.4986844361
0.0514328113.169506073
0.82941474.48695
2.48747158052.6163947582
3.8283056.1890354156
7.94688211.74033
7.538446-6.432471
3.7876107693-5.54714
1.82244086274.34841
1.05068171021.5851967335
0.90526122.368151
0.43037626.381937
0.93106047.720172
0.88311564.887479
1.74748122693.473517
2.0883445741.800711
2.07552838335.992757
3.02768754964.1683225632
2.9459095.147196
3.439779525.052799
3.43418955812.3165931702
4.5285634995-1.3730785847
3.22291515.0943746567
3.742896-0.798896
2.7978746891-14.9692277908
1.703813.5682315826
2.06999516498.746055
3.63149070742.3110244274
3.609901-3.4791407585
3.90778714.09605
3.073943615-3.4921572208
2.564726-2.1302621365
2.3092830.6456831
2.045359-1.105868
1.7740278244-8.800473
1.67057728771.1919534206
1.526315093-14.55667
1.85314834127.903409481
1.88252520562.2446427345
2.8541986942-11.5977525711
2.822395-21.8640575409
2.37972235684.577512
1.9669923782-6.516522
2.63253513.5642137527
2.7760963443.8169956207
3.27403163918.995739
3.4321490.6180823445
4.80956840522.171329
4.24031972892.8292126656
4.8249244696.4608635902
2.63518238073.003842
4.39339637764.8901615143
4.3223547.847241
5.89810037614.178603
4.35247755057.783821
4.944522-1.8546527624
3.6528843.5838816166
3.6991795.97447
2.2330381872.865909338
2.08086633684.441267
-1.0184029341-1.7781077623
-8.925352-0.3495439
-3.4403786659-10.37297
-2.696162-1.4569555521
-4.885533-12.993262291
-14.50788-10.742609024
IPD Returns
FT Returns
IPD versus FT Returns 1987-2008
Figure 1 & 3
IPD ReturnsIPD ReturnsLIBORFT ReturnsGDP GrowthLIB REGFT REGGDP REGFT 1FT2AR-TARTAR-TAR
1986Q411.251.706.25-1.54-0.41-13.33-1.2LIBOR6.25FT1-13.33
1987Q12.442.4410.0018.840.506.25-1.54-0.41-13.33-1.2FT-1.54FT2-1.2
1987Q22.722.729.2515.261.106.25-1.54-0.41-13.33-1.2GDP-0.41
1987Q34.954.9510.385.622.206.25-1.54-0.41-13.33-1.2
1987Q45.625.628.94-32.000.906.25-1.54-0.41-13.33-1.2
1988Q15.205.208.694.051.706.25-1.54-0.41-13.33-1.2
1988Q28.038.039.888.310.506.25-1.54-0.41-13.33-1.2
1988Q37.267.2611.94-0.421.406.25-1.54-0.41-13.33-1.2
1988Q46.696.6913.25-1.020.706.25-1.54-0.41-13.33-1.2
1989Q14.794.7913.0615.840.406.25-1.54-0.41-13.33-1.2
1989Q25.175.1714.253.750.606.25-1.54-0.41-13.33-1.2
1989Q34.214.2114.697.150.106.25-1.54-0.41-13.33-1.2
1989Q41.281.2815.164.060.106.25-1.54-0.41-13.33-1.2
1990Q1-0.09-0.0915.25-6.530.806.25-1.54-0.41-13.33-1.2
1990Q2-2.36-2.3614.976.270.506.25-1.54-0.41-13.33-1.2
1990Q3-2.14-2.1414.97-18.13-1.206.25-1.54-0.41-13.33-1.2
1990Q4-2.03-2.0314.068.15-0.606.25-1.54-0.41-13.33-1.2
1991Q1-1.68-1.6812.4415.46-0.106.25-1.54-0.41-13.33-1.2
1991Q2-0.09-0.0911.31-1.26-0.306.25-1.54-0.41-13.33-1.2
1991Q3-0.05-0.0510.3410.17-0.406.25-1.54-0.41-13.33-1.2
1991Q41.061.0610.94-5.510.106.25-1.54-0.41-13.33-1.2
1992Q10.300.3010.81-0.140.106.25-1.54-0.41-13.33-1.2
1992Q20.390.3910.135.10-0.206.25-1.54-0.41-13.33-1.2
1992Q3-0.82-0.829.000.500.506.25-1.54-0.41-13.33-1.2
1992Q40.050.057.0013.170.606.25-1.54-0.41-13.33-1.2
1993Q10.830.835.944.490.606.25-1.54-0.41-13.33-1.2
1993Q22.492.495.972.620.506.25-1.54-0.41-13.33-1.2
1993Q33.833.836.006.190.906.25-1.54-0.41-13.33-1.2
1993Q47.957.955.3111.740.906.25-1.54-0.41-13.33-1.2
1994Q17.547.545.34-6.431.106.25-1.54-0.41-13.33-1.2
1994Q23.793.795.16-5.551.406.25-1.54-0.41-13.33-1.2
1994Q31.821.825.854.351.406.25-1.54-0.41-13.33-1.2
1994Q41.051.056.561.590.706.25-1.54-0.41-13.33-1.2
1995Q10.910.916.632.370.406.25-1.54-0.41-13.33-1.2
1995Q20.430.436.916.380.506.25-1.54-0.41-13.33-1.2
1995Q30.930.936.787.721.106.25-1.54-0.41-13.33-1.2
1995Q40.880.886.504.890.506.25-1.54-0.41-13.33-1.2
1996Q11.751.756.063.471.006.25-1.54-0.41-13.33-1.2
1996Q22.092.095.781.800.406.25-1.54-0.41-13.33-1.2
1996Q32.082.085.885.990.706.25-1.54-0.41-13.33-1.2
1996Q43.033.036.474.170.806.25-1.54-0.41-13.33-1.2
1997Q12.952.956.315.150.806.25-1.54-0.41-13.33-1.2
1997Q23.443.446.845.050.806.25-1.54-0.41-13.33-1.2
1997Q33.433.437.2512.321.006.25-1.54-0.41-13.33-1.2
1997Q44.534.537.56-1.371.206.25-1.54-0.41-13.33-1.2
1998Q13.223.227.5315.090.806.25-1.54-0.41-13.33-1.2
1998Q23.743.747.81-0.800.706.25-1.54-0.41-13.33-1.2
1998Q32.802.807.31-14.970.906.25-1.54-0.41-13.33-1.2
1998Q41.701.706.1913.571.106.25-1.54-0.41-13.33-1.2
1999Q12.072.075.228.750.506.25-1.54-0.41-13.33-1.2
1999Q23.633.635.132.310.806.25-1.54-0.41-13.33-1.2
1999Q33.613.615.47-3.481.306.25-1.54-0.41-13.33-1.2
1999Q43.913.916.0014.101.106.25-1.54-0.41-13.33-1.2
2000Q13.073.076.22-3.491.106.25-1.54-0.41-13.33-1.2
2000Q22.562.566.16-2.131.006.25-1.54-0.41-13.33-1.2
2000Q32.312.316.130.650.506.25-1.54-0.41-13.33-1.2
2000Q42.052.055.84-1.110.406.25-1.54-0.41-13.33-1.2
2001Q11.771.775.47-8.801.206.25-1.54-0.41-13.33-1.2
2001Q21.671.675.251.190.206.25-1.54-0.41-13.33-1.2
2001Q31.531.534.47-14.560.406.25-1.54-0.41-13.33-1.2
2001Q41.851.854.067.900.306.25-1.54-0.41-13.33-1.2
2002Q11.881.884.162.240.806.25-1.54-0.41-13.33-1.2
2002Q22.852.854.09-11.600.406.25-1.54-0.41-13.33-1.2
2002Q32.822.823.91-21.860.706.25-1.54-0.41-13.33-1.2
2002Q42.382.383.964.580.606.25-1.54-0.41-13.33-1.2
2003Q11.971.973.61-6.520.606.25-1.54-0.41-13.33-1.2
2003Q22.632.633.5913.560.906.25-1.54-0.41-13.33-1.2
2003Q32.782.783.673.820.706.25-1.54-0.41-13.33-1.2
2003Q43.273.273.989.000.906.25-1.54-0.41-13.33-1.2
2004Q13.433.434.330.621.006.25-1.54-0.41-13.33-1.2
2004Q24.814.814.792.170.606.25-1.54-0.41-13.33-1.2
2004Q34.244.244.862.830.106.25-1.54-0.41-13.33-1.2
2004Q44.824.824.846.460.806.25-1.54-0.41-13.33-1.2
2005Q12.642.644.933.000.306.25-1.54-0.41-13.33-1.2
2005Q24.394.394.734.890.706.25-1.54-0.41-13.33-1.2
2005Q34.324.324.557.850.606.25-1.54-0.41-13.33-1.2
2005Q45.905.904.594.180.706.25-1.54-0.41-13.33-1.2
2006Q14.354.354.567.781.106.25-1.54-0.41-13.33-1.2
2006Q24.944.944.73-1.850.406.25-1.54-0.41-13.33-1.2
2006Q33.653.655.053.580.506.25-1.54-0.41-13.33-1.2
2006Q43.703.705.295.970.806.25-1.54-0.41-13.33-1.2
2007Q12.232.235.582.870.706.25-1.54-0.41-13.33-1.2
2007Q22.082.085.984.440.606.25-1.54-0.41-13.33-1.2
2007Q3-1.02-1.026.28-1.780.506.25-1.54-0.41-13.33-1.2
2007Q4-8.93-8.935.95-0.350.506.25-1.54-0.41-13.33-1.2
2008Q1-3.44-3.446.02-10.370.706.25-1.54-0.41-13.33-1.2
2008Q2-2.70-2.705.94-1.46-0.106.25-1.54-0.41-13.33-1.2
2008Q3-4.89-4.896.30-12.99-0.706.25-1.54-0.41-13.33-1.2
2008Q4-14.51-14.512.83-10.74-1.806.25-1.54-0.41-13.33-1.2
Figure 1 & 3
IPD Returns
Figure 2
LIBOR
LIB REG
LIBOR Regime
Figure 4
FT Returns
FT REG
FT Returns Regime
Sheet2
GDP Growth
GDP REG
GDP Growth Regime
Sheet3
FT Returns
FT 1
FT2
FT Return Regimes (TAR-TAR)
IPD Returns
FT Returns
IPD versus FT Returns 1987-2008
IPD ReturnsAR-TARAR
1986Q4
1987Q12.44
1987Q22.723.047.48
1987Q34.957.4742.57
1987Q45.626.3716.88
1988Q15.204.72-1.92
1988Q28.0311.2255.86
1988Q37.266.40-5.71
1988Q46.696.04-3.04
1989Q14.792.65-27.22
1989Q25.175.6011.64
1989Q34.213.12-12.10
1989Q41.28-2.02-48.11
1990Q1-0.09-1.64-23.25
1990Q2-2.36-4.91-40.63
1990Q3-2.14-1.901.45
1990Q4-2.03-1.90-0.10
1991Q1-1.68-1.284.29
1991Q2-0.091.7126.77
1991Q3-0.05-0.010.55
1991Q41.062.3219.83
1992Q10.30-0.56-12.61
1992Q20.390.481.87
1992Q3-0.82-2.17-21.13
1992Q40.051.0314.73
1993Q10.831.7113.97
1993Q22.494.3630.49
1993Q33.835.3426.47
1993Q47.9512.5977.50
1994Q17.547.080.64
1994Q23.79-0.44-59.56
1994Q31.82-0.39-31.36
1994Q41.050.18-11.98
1995Q10.910.74-1.55
1995Q20.43-0.11-7.59
1995Q30.931.509.39
1995Q40.880.830.07
1996Q11.752.7216.34
1996Q22.092.477.84
1996Q32.082.061.86
1996Q43.034.1019.11
1997Q12.952.851.56
1997Q23.444.0011.78
1997Q33.433.433.34
1997Q44.535.7623.01
1998Q13.221.75-18.83
1998Q23.744.3312.52
1998Q32.801.73-13.16
1998Q41.700.47-16.77
1999Q12.072.488.25
1999Q23.635.3930.00
1999Q33.613.593.25
1999Q43.914.248.94
2000Q13.072.13-11.01
2000Q22.561.99-6.03
2000Q32.312.02-2.00
2000Q42.051.75-2.41
2001Q11.771.47-2.81
2001Q21.671.55-0.08
2001Q31.531.36-0.91
2001Q41.852.227.37
2002Q11.881.922.38
2002Q22.853.9519.26
2002Q32.822.792.29
2002Q42.381.88-5.10
2003Q11.971.50-5.00
2003Q22.633.3813.87
2003Q32.782.945.20
2003Q43.273.8411.68
2004Q13.433.616.10
2004Q24.816.3628.07
2004Q34.243.60-5.37
2004Q44.825.4814.70
2005Q12.640.17-34.34
2005Q24.396.3834.09
2005Q34.324.243.12
2005Q45.907.6832.51
2006Q14.352.61-21.75
2006Q24.945.6114.94
2006Q33.652.20-18.16
2006Q43.703.754.48
2007Q12.230.58-22.53
2007Q22.081.91-0.49
2007Q3-1.02-4.51-53.36
2007Q4-8.93-17.84-142.46
2008Q1-3.442.7589.19
2008Q2-2.70-1.869.87
2008Q3-4.89-7.36-41.86
2008Q4-14.51-25.36-177.01
2.141.92-1.15
3.274.8134.11
0.8130.5140.098
2.7249483.04222732097.475116
4.9526476867.465454016542.57331
5.61940240866.371490088316.8793354034
5.19769763954.7220220266-1.9239122868
8.02972611.224204518455.8560943604
7.2615376.3950332274-5.711397
6.6858616.0365085284-3.0359566212
4.79012632372.6517707251-27.2244224548
5.1729775.604825874911.6384325027
4.20709753043.1176023614-12.1043548584
1.2822022438-2.0170285449-48.11247
-0.08922204-1.6361646749-23.2493858337
-2.3555314541-4.9118888834-40.62822
-2.1429033279-1.9030625161.447891
-2.0286085606-1.8996860596-0.09843776
-1.6751872301-1.27653414324.293277
-0.085200851.708276011526.7659683228
-0.04989183-0.01006387220.5463953
1.06174767022.315657607319.83475
0.2975316346-0.5644907036-12.608297348
0.38536563520.48444085351.8686773777
-0.8175488-2.1744152693-21.1319732666
0.051432811.03162888614.7265090942
0.82941471.706964681513.9677171707
2.48747158054.357730777430.48819
3.8283055.340741674426.47186
7.94688212.592564909277.50005
7.5384467.07773732690.6409188509
3.7876107693-0.4432658482-59.55527
1.8224408627-0.3942364628-31.3647
1.05068171020.1801508681-11.9825344086
0.90526120.7412294048-1.550552
0.4303762-0.1052857843-7.589326
0.93106041.49582343129.386451
0.88311560.82903470310.073439315
1.74748122692.722470554616.3446044922
2.0883445742.4728324757.844733
2.07552838332.0610719441.8590914011
3.02768754964.101706456119.10744
2.9459092.85366422461.5648614168
3.439779523.996856839311.7801017761
3.4341895583.42788417853.339788
4.52856349955.762998187923.0099925995
3.2229151.7501663008-18.8264465332
3.7428964.329425484512.5241613388
2.79787468911.7319071588-13.1613349915
1.70380.4697028629-16.7725734711
2.06999516492.48305691388.25418
3.63149070745.392830401930.0015144348
3.6099013.58554818723.2453007698
3.9077874.24379720438.938385
3.0739436152.1333828429-11.0077285767
2.5647261.9903374258-6.034776
2.3092832.0211477583-2.004553
2.0453591.7476573384-2.4117052555
1.77402782441.4679709982-2.808121
1.67057728771.5538868894-0.07646142
1.5263150931.3635898576-0.9099388
1.85314834122.22181053577.372601
1.88252520561.91566179552.3786323071
2.85419869423.950229415419.2635
2.8223952.78652098852.2853043079
2.37972235681.8803953482-5.095986
1.96699237821.5014401723-5.0030565262
2.6325353.383255451113.872
2.7760963442.93803103225.2005133629
3.27403163913.835693953611.6829986572
3.4321493.6105026216.102383
4.80956840526.363273432228.0709762573
4.24031972893.5982171661-5.372961
4.8249244695.484348403514.6975336075
2.63518238070.1651915573-34.3444633484
4.39339637766.376631052134.08554
4.3223544.24221943913.1226115227
5.89810037617.675514761932.50879
4.35247755052.6090420034-21.74949646
4.9445225.612337796714.9427709579
3.6528842.1959388994-18.15987
3.6991793.75139895134.480998
2.2330381870.5792569618-22.52667
2.08086633681.9092191481-0.488962
-1.0184029341-4.514324531-53.3578453064
-8.925352-17.8442524211-142.4553222656
-3.44037866592.746575438889.18805
-2.696162-1.85669860149.871923
-4.885533-7.3551052422-41.8589057922
-14.50788-25.3617193248-177.0069122314
IPD Returns
AR-TAR
AR
2.7249483.0422273209
4.9526476867.4654540165
5.61940240866.3714900883
5.19769763954.7220220266
8.02972611.2242045184
7.2615376.3950332274
6.6858616.0365085284
4.79012632372.6517707251
5.1729775.6048258749
4.20709753043.1176023614
1.2822022438-2.0170285449
-0.08922204-1.6361646749
-2.3555314541-4.9118888834
-2.1429033279-1.903062516
-2.0286085606-1.8996860596
-1.6751872301-1.2765341432
-0.085200851.7082760115
-0.04989183-0.0100638722
1.06174767022.3156576073
0.2975316346-0.5644907036
0.38536563520.4844408535
-0.8175488-2.1744152693
0.051432811.031628886
0.82941471.7069646815
2.48747158054.3577307774
3.8283055.3407416744
7.94688212.5925649092
7.5384467.0777373269
3.7876107693-0.4432658482
1.8224408627-0.3942364628
1.05068171020.1801508681
0.90526120.7412294048
0.4303762-0.1052857843
0.93106041.4958234312
0.88311560.8290347031
1.74748122692.7224705546
2.0883445742.472832475
2.07552838332.061071944
3.02768754964.1017064561
2.9459092.8536642246
3.439779523.9968568393
3.4341895583.4278841785
4.52856349955.7629981879
3.2229151.7501663008
3.7428964.3294254845
2.79787468911.7319071588
1.70380.4697028629
2.06999516492.4830569138
3.63149070745.3928304019
3.6099013.5855481872
3.9077874.2437972043
3.0739436152.1333828429
2.5647261.9903374258
2.3092832.0211477583
2.0453591.7476573384
1.77402782441.4679709982
1.67057728771.5538868894
1.5263150931.3635898576
1.85314834122.2218105357
1.88252520561.9156617955
2.85419869423.9502294154
2.8223952.7865209885
2.37972235681.8803953482
1.96699237821.5014401723
2.6325353.3832554511
2.7760963442.9380310322
3.27403163913.8356939536
3.4321493.610502621
4.80956840526.3632734322
4.24031972893.5982171661
4.8249244695.4843484035
2.63518238070.1651915573
4.39339637766.3766310521
4.3223544.2422194391
5.89810037617.6755147619
4.35247755052.6090420034
4.9445225.6123377967
3.6528842.1959388994
3.6991793.7513989513
2.2330381870.5792569618
2.08086633681.9092191481
-1.0184029341-4.514324531
-8.925352-17.8442524211
-3.44037866592.7465754388
-2.696162-1.8566986014
-4.885533-7.3551052422
-14.50788-25.3617193248
IPD Returns
AR-TAR
IPD ReturnsTAR-TARARalpha 0.8
1986Q4
1987Q12.44
1987Q22.723.457.483.85
1987Q34.9510.6742.5713.86
1987Q45.627.3316.888.29
1988Q15.20-5.34-1.923.51
1988Q28.0315.3055.8619.36
1988Q37.265.29-5.714.19
1988Q46.695.21-3.044.38
1989Q14.79-0.08-27.22-2.79
1989Q25.176.1611.646.70
1989Q34.211.73-12.100.34
1989Q41.28-6.23-48.11-10.42
1990Q1-0.09-3.61-23.25-5.57
1990Q2-2.36-8.17-40.63-11.42
1990Q3-2.14-1.601.45-1.29
1990Q4-2.030.83-0.10-1.57
1991Q1-1.68-0.774.29-0.26
1991Q2-0.094.0026.776.27
1991Q3-0.050.040.550.09
1991Q41.063.9119.835.51
1992Q10.30-1.66-12.61-2.76
1992Q20.390.611.870.74
1992Q3-0.82-3.91-21.13-5.63
1992Q40.052.2814.733.53
1993Q10.832.8313.973.94
1993Q22.496.7430.499.12
1993Q33.837.2726.479.19
1993Q47.9518.5277.5024.42
1994Q17.546.490.645.90
1994Q23.79-5.84-59.56-11.22
1994Q31.82-3.22-31.36-6.04
1994Q41.05-0.93-11.98-2.04
1995Q10.910.53-1.550.32
1995Q20.43-0.79-7.59-1.47
1995Q30.932.229.392.93
1995Q40.880.760.070.69
1996Q11.753.9716.345.20
1996Q22.092.967.843.45
1996Q32.082.041.862.02
1996Q43.035.4719.116.84
1997Q12.952.741.562.62
1997Q23.444.7111.785.42
1997Q33.433.423.343.41
1997Q44.537.3423.018.91
1998Q13.22-0.13-18.83-2.00
1998Q23.745.0812.525.82
1998Q32.800.37-13.16-0.98
1998Q41.70-25.63-16.77-2.67
1999Q12.073.018.253.53
1999Q23.637.6430.009.88
1999Q33.613.553.253.52
1999Q43.914.678.945.10
2000Q13.070.93-11.01-0.26
2000Q22.561.26-6.030.53
2000Q32.311.65-2.001.29
2000Q42.051.37-2.410.99
2001Q11.771.08-2.810.69
2001Q21.671.41-0.081.26
2001Q31.531.16-0.910.95
2001Q41.8510.027.373.16
2002Q11.881.962.382.00
2002Q22.855.3519.266.74
2002Q32.822.742.292.70
2002Q42.38-8.68-5.100.61
2003Q11.970.91-5.000.32
2003Q22.634.3413.875.29
2003Q32.783.145.203.35
2003Q43.274.5511.685.27
2004Q13.433.846.104.06
2004Q24.818.3428.0710.32
2004Q34.242.78-5.371.96
2004Q44.826.3314.707.16
2005Q12.64-2.99-34.34-6.12
2005Q24.398.9134.0911.43
2005Q34.324.143.124.04
2005Q45.909.9432.5112.20
2006Q14.350.39-21.75-1.83
2006Q24.946.4614.947.31
2006Q33.650.34-18.16-1.51
2006Q43.703.824.483.88
2007Q12.23-1.53-22.53-3.63
2007Q22.081.69-0.491.47
2007Q3-1.02-8.97-53.36-13.42
2007Q4-8.93-29.22-142.46-40.55
2008Q1-3.4410.6489.1918.50
2008Q2-2.70-0.799.870.28
2008Q3-4.89-10.50-41.86-13.64
2008Q4-14.51-39.21-177.01-53.00
2.141.25-1.151.36
3.277.9534.119.82
0.8130.1990.0980.222
-1.999-2.514-2.154-2.721
8.06510.31010.84413.726
IPDTAR TARAR ARAlpha 0.8
IPD1.000
TAR TAR0.7371.000
AR AR0.6180.8891.000
Alpha 0.80.7620.9190.9801.000
2.62
-53.00
24.42
8.0318.5289.1924.42
-14.51-39.21-177.01-53.00
IPD Returns
TAR-TAR
AR
IPD Returns
TAR-TAR
alpha 0.8
IPD Returns
TAR-TAR
-
Smoothing and Underlying Return ProcessBasic Smoothing Model
Return Process
Note the Time Subscripts
-
Possible ModelsAR ModelAR return process, single smoothing parameterAR-TAR ModelRegime-based return, single smoothing processTAR-ARRegime-based smoothing, single return processTAR-TARRegime-based smoothing and return processes
-
Defining Regimes and ModellingRegime Variables TestedMacro: GDP, Employment, Inflation, /$Asset & Cap Market: Equity Market, Interest RateEndogenous: Cap RateAnalysis Quarterly, 1987Q1 2008Q4 Recursively Estimate and Minimise SSEBest Regime Models: AR-TARFT Returns, LIBORBest Regime Model: TAR-TARFT Returns for Both Processes
-
AR-TAR
Model
[Min,Max]
SSE
TAR
LIBOR
0.51**
(0.07)
-1.25*
(0.48)
1.27**
(0.10)
2.38**
(0.65)
0.18
(0.11)
6.25
0.56
[2.83,15.25]
233.45
Inflation rate
0.77**
(0.09)
0.25
(1.67)
-0.09
(0.15)
-0.22
(1.08)
0.95**
(0.23)
0.94
0.33
[-0.57,2.73]
259.44
Real interest
0.72**
(0.14)
-0.98
(0.75)
0.98**
(0.12)
3.01**
(1.13)
-0.17
(0.09)
5.12
0.57
[2.67,13.81]
242.68
FT returns
0.53**
(0.09)
2.22**
(0.32)
0.31**
(0.08)
-4.05**
(0.94)
1.77**
(0.24)
-1.54
0.76
[-32.00,18.84]
179.91
Exchange rate
0.93**
(0.02)
-40.54
(235.98)
1.70
(7.65)
1.33
(2.20)
0.02
(0.10)
1.95
0.05
[1.41,2.04]
240.19
Initial Yield
0.92**
(0.04)
1.60
(2.18)
0.02
(0.10)
-17.40**
(3.85)
1.76**
(0.32)
4.64
0.95
[4.57,9.09]
255.33
GDP Growth
0.81**
(0.12)
1.72
(0.99)
0.11
(0.08)
5.18
(6.66)
4.27*
(1.86)
-0.41
0.94
[-1.80,2.20]
208.52
AR
0.94**
(0.04)
-1.35
(2.82)
0.12
(0.15)
309.53
_1335081022.unknown
_1335081024.unknown
_1335081026.unknown
_1335081027.unknown
_1335081025.unknown
_1335081023.unknown
_1335081021.unknown
-
AR-TAR: FT Returns Regimes
Chart1
18.841917038-1.54
15.2607927322-1.54
5.616584-1.54
-32.0026550293-1.54
4.0549674034-1.54
8.310058-1.54
-0.4158257-1.54
-1.0190192461-1.54
15.8391513824-1.54
3.7536697388-1.54
7.152185-1.54
4.0634436607-1.54
-6.530186-1.54
6.268623-1.54
-18.13032341-1.54
8.147772-1.54
15.4552135468-1.54
-1.2575266361-1.54
10.16984272-1.54
-5.514645-1.54
-0.1393856108-1.54
5.096318-1.54
0.4986844361-1.54
13.169506073-1.54
4.48695-1.54
2.6163947582-1.54
6.1890354156-1.54
11.74033-1.54
-6.432471-1.54
-5.54714-1.54
4.34841-1.54
1.5851967335-1.54
2.368151-1.54
6.381937-1.54
7.720172-1.54
4.887479-1.54
3.473517-1.54
1.800711-1.54
5.992757-1.54
4.1683225632-1.54
5.147196-1.54
5.052799-1.54
12.3165931702-1.54
-1.3730785847-1.54
15.0943746567-1.54
-0.798896-1.54
-14.9692277908-1.54
13.5682315826-1.54
8.746055-1.54
2.3110244274-1.54
-3.4791407585-1.54
14.09605-1.54
-3.4921572208-1.54
-2.1302621365-1.54
0.6456831-1.54
-1.105868-1.54
-8.800473-1.54
1.1919534206-1.54
-14.55667-1.54
7.903409481-1.54
2.2446427345-1.54
-11.5977525711-1.54
-21.8640575409-1.54
4.577512-1.54
-6.516522-1.54
13.5642137527-1.54
3.8169956207-1.54
8.995739-1.54
0.6180823445-1.54
2.171329-1.54
2.8292126656-1.54
6.4608635902-1.54
3.003842-1.54
4.8901615143-1.54
7.847241-1.54
4.178603-1.54
7.783821-1.54
-1.8546527624-1.54
3.5838816166-1.54
5.97447-1.54
2.865909338-1.54
4.441267-1.54
-1.7781077623-1.54
-0.3495439-1.54
-10.37297-1.54
-1.4569555521-1.54
-12.993262291-1.54
-10.742609024-1.54
FT Returns
FT REG
FT Returns Regime
Figure 1 & 3
IPD ReturnsIPD ReturnsLIBORFT ReturnsGDP GrowthLIB REGFT REGGDP REGFT 1FT2AR-TARTAR-TAR
1986Q411.251.706.25-1.54-0.41-13.33-1.2LIBOR6.25FT1-13.33
1987Q12.442.4410.0018.840.506.25-1.54-0.41-13.33-1.2FT-1.54FT2-1.2
1987Q22.722.729.2515.261.106.25-1.54-0.41-13.33-1.2GDP-0.41
1987Q34.954.9510.385.622.206.25-1.54-0.41-13.33-1.2
1987Q45.625.628.94-32.000.906.25-1.54-0.41-13.33-1.2
1988Q15.205.208.694.051.706.25-1.54-0.41-13.33-1.2
1988Q28.038.039.888.310.506.25-1.54-0.41-13.33-1.2
1988Q37.267.2611.94-0.421.406.25-1.54-0.41-13.33-1.2
1988Q46.696.6913.25-1.020.706.25-1.54-0.41-13.33-1.2
1989Q14.794.7913.0615.840.406.25-1.54-0.41-13.33-1.2
1989Q25.175.1714.253.750.606.25-1.54-0.41-13.33-1.2
1989Q34.214.2114.697.150.106.25-1.54-0.41-13.33-1.2
1989Q41.281.2815.164.060.106.25-1.54-0.41-13.33-1.2
1990Q1-0.09-0.0915.25-6.530.806.25-1.54-0.41-13.33-1.2
1990Q2-2.36-2.3614.976.270.506.25-1.54-0.41-13.33-1.2
1990Q3-2.14-2.1414.97-18.13-1.206.25-1.54-0.41-13.33-1.2
1990Q4-2.03-2.0314.068.15-0.606.25-1.54-0.41-13.33-1.2
1991Q1-1.68-1.6812.4415.46-0.106.25-1.54-0.41-13.33-1.2
1991Q2-0.09-0.0911.31-1.26-0.306.25-1.54-0.41-13.33-1.2
1991Q3-0.05-0.0510.3410.17-0.406.25-1.54-0.41-13.33-1.2
1991Q41.061.0610.94-5.510.106.25-1.54-0.41-13.33-1.2
1992Q10.300.3010.81-0.140.106.25-1.54-0.41-13.33-1.2
1992Q20.390.3910.135.10-0.206.25-1.54-0.41-13.33-1.2
1992Q3-0.82-0.829.000.500.506.25-1.54-0.41-13.33-1.2
1992Q40.050.057.0013.170.606.25-1.54-0.41-13.33-1.2
1993Q10.830.835.944.490.606.25-1.54-0.41-13.33-1.2
1993Q22.492.495.972.620.506.25-1.54-0.41-13.33-1.2
1993Q33.833.836.006.190.906.25-1.54-0.41-13.33-1.2
1993Q47.957.955.3111.740.906.25-1.54-0.41-13.33-1.2
1994Q17.547.545.34-6.431.106.25-1.54-0.41-13.33-1.2
1994Q23.793.795.16-5.551.406.25-1.54-0.41-13.33-1.2
1994Q31.821.825.854.351.406.25-1.54-0.41-13.33-1.2
1994Q41.051.056.561.590.706.25-1.54-0.41-13.33-1.2
1995Q10.910.916.632.370.406.25-1.54-0.41-13.33-1.2
1995Q20.430.436.916.380.506.25-1.54-0.41-13.33-1.2
1995Q30.930.936.787.721.106.25-1.54-0.41-13.33-1.2
1995Q40.880.886.504.890.506.25-1.54-0.41-13.33-1.2
1996Q11.751.756.063.471.006.25-1.54-0.41-13.33-1.2
1996Q22.092.095.781.800.406.25-1.54-0.41-13.33-1.2
1996Q32.082.085.885.990.706.25-1.54-0.41-13.33-1.2
1996Q43.033.036.474.170.806.25-1.54-0.41-13.33-1.2
1997Q12.952.956.315.150.806.25-1.54-0.41-13.33-1.2
1997Q23.443.446.845.050.806.25-1.54-0.41-13.33-1.2
1997Q33.433.437.2512.321.006.25-1.54-0.41-13.33-1.2
1997Q44.534.537.56-1.371.206.25-1.54-0.41-13.33-1.2
1998Q13.223.227.5315.090.806.25-1.54-0.41-13.33-1.2
1998Q23.743.747.81-0.800.706.25-1.54-0.41-13.33-1.2
1998Q32.802.807.31-14.970.906.25-1.54-0.41-13.33-1.2
1998Q41.701.706.1913.571.106.25-1.54-0.41-13.33-1.2
1999Q12.072.075.228.750.506.25-1.54-0.41-13.33-1.2
1999Q23.633.635.132.310.806.25-1.54-0.41-13.33-1.2
1999Q33.613.615.47-3.481.306.25-1.54-0.41-13.33-1.2
1999Q43.913.916.0014.101.106.25-1.54-0.41-13.33-1.2
2000Q13.073.076.22-3.491.106.25-1.54-0.41-13.33-1.2
2000Q22.562.566.16-2.131.006.25-1.54-0.41-13.33-1.2
2000Q32.312.316.130.650.506.25-1.54-0.41-13.33-1.2
2000Q42.052.055.84-1.110.406.25-1.54-0.41-13.33-1.2
2001Q11.771.775.47-8.801.206.25-1.54-0.41-13.33-1.2
2001Q21.671.675.251.190.206.25-1.54-0.41-13.33-1.2
2001Q31.531.534.47-14.560.406.25-1.54-0.41-13.33-1.2
2001Q41.851.854.067.900.306.25-1.54-0.41-13.33-1.2
2002Q11.881.884.162.240.806.25-1.54-0.41-13.33-1.2
2002Q22.852.854.09-11.600.406.25-1.54-0.41-13.33-1.2
2002Q32.822.823.91-21.860.706.25-1.54-0.41-13.33-1.2
2002Q42.382.383.964.580.606.25-1.54-0.41-13.33-1.2
2003Q11.971.973.61-6.520.606.25-1.54-0.41-13.33-1.2
2003Q22.632.633.5913.560.906.25-1.54-0.41-13.33-1.2
2003Q32.782.783.673.820.706.25-1.54-0.41-13.33-1.2
2003Q43.273.273.989.000.906.25-1.54-0.41-13.33-1.2
2004Q13.433.434.330.621.006.25-1.54-0.41-13.33-1.2
2004Q24.814.814.792.170.606.25-1.54-0.41-13.33-1.2
2004Q34.244.244.862.830.106.25-1.54-0.41-13.33-1.2
2004Q44.824.824.846.460.806.25-1.54-0.41-13.33-1.2
2005Q12.642.644.933.000.306.25-1.54-0.41-13.33-1.2
2005Q24.394.394.734.890.706.25-1.54-0.41-13.33-1.2
2005Q34.324.324.557.850.606.25-1.54-0.41-13.33-1.2
2005Q45.905.904.594.180.706.25-1.54-0.41-13.33-1.2
2006Q14.354.354.567.781.106.25-1.54-0.41-13.33-1.2
2006Q24.944.944.73-1.850.406.25-1.54-0.41-13.33-1.2
2006Q33.653.655.053.580.506.25-1.54-0.41-13.33-1.2
2006Q43.703.705.295.970.806.25-1.54-0.41-13.33-1.2
2007Q12.232.235.582.870.706.25-1.54-0.41-13.33-1.2
2007Q22.082.085.984.440.606.25-1.54-0.41-13.33-1.2
2007Q3-1.02-1.026.28-1.780.506.25-1.54-0.41-13.33-1.2
2007Q4-8.93-8.935.95-0.350.506.25-1.54-0.41-13.33-1.2
2008Q1-3.44-3.446.02-10.370.706.25-1.54-0.41-13.33-1.2
2008Q2-2.70-2.705.94-1.46-0.106.25-1.54-0.41-13.33-1.2
2008Q3-4.89-4.896.30-12.99-0.706.25-1.54-0.41-13.33-1.2
2008Q4-14.51-14.512.83-10.74-1.806.25-1.54-0.41-13.33-1.2
Figure 1 & 3
IPD Returns
Figure 2
LIBOR
LIB REG
LIBOR Regime
Figure 4
FT Returns
FT REG
FT Returns Regime
Sheet2
GDP Growth
GDP REG
GDP Growth Regime
Sheet3
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
000
FT Returns
FT 1
FT2
FT Return Regimes (TAR-TAR)
IPD ReturnsAR-TARAR
1986Q4
1987Q12.44
1987Q22.723.047.48
1987Q34.957.4742.57
1987Q45.626.3716.88
1988Q15.204.72-1.92
1988Q28.0311.2255.86
1988Q37.266.40-5.71
1988Q46.696.04-3.04
1989Q14.792.65-27.22
1989Q25.175.6011.64
1989Q34.213.12-12.10
1989Q41.28-2.02-48.11
1990Q1-0.09-1.64-23.25
1990Q2-2.36-4.91-40.63
1990Q3-2.14-1.901.45
1990Q4-2.03-1.90-0.10
1991Q1-1.68-1.284.29
1991Q2-0.091.7126.77
1991Q3-0.05-0.010.55
1991Q41.062.3219.83
1992Q10.30-0.56-12.61
1992Q20.390.481.87
1992Q3-0.82-2.17-21.13
1992Q40.051.0314.73
1993Q10.831.7113.97
1993Q22.494.3630.49
1993Q33.835.3426.47
1993Q47.9512.5977.50
1994Q17.547.080.64
1994Q23.79-0.44-59.56
1994Q31.82-0.39-31.36
1994Q41.050.18-11.98
1995Q10.910.74-1.55
1995Q20.43-0.11-7.59
1995Q30.931.509.39
1995Q40.880.830.07
1996Q11.752.7216.34
1996Q22.092.477.84
1996Q32.082.061.86
1996Q43.034.1019.11
1997Q12.952.851.56
1997Q23.444.0011.78
1997Q33.433.433.34
1997Q44.535.7623.01
1998Q13.221.75-18.83
1998Q23.744.3312.52
1998Q32.801.73-13.16
1998Q41.700.47-16.77
1999Q12.072.488.25
1999Q23.635.3930.00
1999Q33.613.593.25
1999Q43.914.248.94
2000Q13.072.13-11.01
2000Q22.561.99-6.03
2000Q32.312.02-2.00
2000Q42.051.75-2.41
2001Q11.771.47-2.81
2001Q21.671.55-0.08
2001Q31.531.36-0.91
2001Q41.852.227.37
2002Q11.881.922.38
2002Q22.853.9519.26
2002Q32.822.792.29
2002Q42.381.88-5.10
2003Q11.971.50-5.00
2003Q22.633.3813.87
2003Q32.782.945.20
2003Q43.273.8411.68
2004Q13.433.616.10
2004Q24.816.3628.07
2004Q34.243.60-5.37
2004Q44.825.4814.70
2005Q12.640.17-34.34
2005Q24.396.3834.09
2005Q34.324.243.12
2005Q45.907.6832.51
2006Q14.352.61-21.75
2006Q24.945.6114.94
2006Q33.652.20-18.16
2006Q43.703.754.48
2007Q12.230.58-22.53
2007Q22.081.91-0.49
2007Q3-1.02-4.51-53.36
2007Q4-8.93-17.84-142.46
2008Q1-3.442.7589.19
2008Q2-2.70-1.869.87
2008Q3-4.89-7.36-41.86
2008Q4-14.51-25.36-177.01
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IPD Returns
AR-TAR
AR
IPD ReturnsTAR-TARARalpha 0.8
1986Q4
1987Q12.44
1987Q22.723.457.483.85
1987Q34.9510.6742.5713.86
1987Q45.627.3316.888.29
1988Q15.20-5.34-1.923.51
1988Q28.0315.3055.8619.36
1988Q37.265.29-5.714.19
1988Q46.695.21-3.044.38
1989Q14.79-0.08-27.22-2.79
1989Q25.176.1611.646.70
1989Q34.211.73-12.100.34
1989Q41.28-6.23-48.11-10.42
1990Q1-0.09-3.61-23.25-5.57
1990Q2-2.36-8.17-40.63-11.42
1990Q3-2.14-1.601.45-1.29
1990Q4-2.030.83-0.10-1.57
1991Q1-1.68-0.774.29-0.26
1991Q2-0.094.0026.776.27
1991Q3-0.050.040.550.09
1991Q41.063.9119.835.51
1992Q10.30-1.66-12.61-2.76
1992Q20.390.611.870.74
1992Q3-0.82-3.91-21.13-5.63
1992Q40.052.2814.733.53
1993Q10.832.8313.973.94
1993Q22.496.7430.499.12
1993Q33.837.2726.479.19
1993Q47.9518.5277.5024.42
1994Q17.546.490.645.90
1994Q23.79-5.84-59.56-11.22
1994Q31.82-3.22-31.36-6.04
1994Q41.05-0.93-11.98-2.04
1995Q10.910.53-1.550.32
1995Q20.43-0.79-7.59-1.47
1995Q30.932.229.392.93
1995Q40.880.760.070.69
1996Q11.753.9716.345.20
1996Q22.092.967.843.45
1996Q32.082.041.862.02
1996Q43.035.4719.116.84
1997Q12.952.741.562.62
1997Q23.444.7111.785.42
1997Q33.433.423.343.41
1997Q44.537.3423.018.91
1998Q13.22-0.13-18.83-2.00
1998Q23.745.0812.525.82
1998Q32.800.37-13.16-0.98
1998Q41.70-25.63-16.77-2.67
1999Q12.073.018.253.53
1999Q23.637.6430.009.88
1999Q33.613.553.253.52
1999Q43.914.678.945.10
2000Q13.070.93-11.01-0.26
2000Q22.561.26-6.030.53
2000Q32.311.65-2.001.29
2000Q42.051.37-2.410.99
2001Q11.771.08-2.810.69
2001Q21.671.41-0.081.26
2001Q31.531.16-0.910.95
2001Q41.8510.027.373.16
2002Q11.881.962.382.00
2002Q22.855.3519.266.74
2002Q32.822.742.292.70
2002Q42.38-8.68-5.100.61
2003Q11.970.91-5.000.32
2003Q22.634.3413.875.29
2003Q32.783.145.203.35
2003Q43.274.5511.685.27
2004Q13.433.846.104.06
2004Q24.818.3428.0710.32
2004Q34.242.78-5.371.96
2004Q44.826.3314.707.16
2005Q12.64-2.99-34.34-6.12
2005Q24.398.9134.0911.43
2005Q34.324.143.124.04
2005Q45.909.9432.5112.20
2006Q14.350.39-21.75-1.83
2006Q24.946.4614.947.31
2006Q33.650.34-18.16-1.51
2006Q43.703.824.483.88
2007Q12.23-1.53-22.53-3.63
2007Q22.081.69-0.491.47
2007Q3-1.02-8.97-53.36-13.42
2007Q4-8.93-29.22-142.46-40.55
2008Q1-3.4410.6489.1918.50
2008Q2-2.70-0.799.870.28
2008Q3-4.89-10.50-41.86-13.64
2008Q4-14.51-39.21-177.01-53.00
2.141.25-1.151.36
3.277.9534.119.82
0.8130.1990.0980.222
-1.999-2.514-2.154-2.721
8.06510.31010.84413.726
IPDTAR TARAR ARAlpha 0.8
IPD1.000
TAR TAR0.7371.000
AR AR0.6180.8891.000
Alpha 0.80.7620.9190.9801.000
2.62
-53.00
24.42
IPD Returns
TAR-TAR
AR
IPD Returns
TAR-TAR
alpha 0.8
IPD Returns
TAR-TAR
-
AR-TAR versus AR: Fits The AR model appears too volatile particularly across 2008 The AR-TAR model generates more plausible results
Chart5
2.7249483.04222732097.475116
4.9526476867.465454016542.57331
5.61940240866.371490088316.8793354034
5.19769763954.7220220266-1.9239122868
8.02972611.224204518455.8560943604
7.2615376.3950332274-5.711397
6.6858616.0365085284-3.0359566212
4.79012632372.6517707251-27.2244224548
5.1729775.604825874911.6384325027
4.20709753043.1176023614-12.1043548584
1.2822022438-2.0170285449-48.11247
-0.08922204-1.6361646749-23.2493858337
-2.3555314541-4.9118888834-40.62822
-2.1429033279-1.9030625161.447891
-2.0286085606-1.8996860596-0.09843776
-1.6751872301-1.27653414324.293277
-0.085200851.708276011526.7659683228
-0.04989183-0.01006387220.5463953
1.06174767022.315657607319.83475
0.2975316346-0.5644907036-12.608297348
0.38536563520.48444085351.8686773777
-0.8175488-2.1744152693-21.1319732666
0.051432811.03162888614.7265090942
0.82941471.706964681513.9677171707
2.48747158054.357730777430.48819
3.8283055.340741674426.47186
7.94688212.592564909277.50005
7.5384467.07773732690.6409188509
3.7876107693-0.4432658482-59.55527
1.8224408627-0.3942364628-31.3647
1.05068171020.1801508681-11.9825344086
0.90526120.7412294048-1.550552
0.4303762-0.1052857843-7.589326
0.93106041.49582343129.386451
0.88311560.82903470310.073439315
1.74748122692.722470554616.3446044922
2.0883445742.4728324757.844733
2.07552838332.0610719441.8590914011
3.02768754964.101706456119.10744
2.9459092.85366422461.5648614168
3.439779523.996856839311.7801017761
3.4341895583.42788417853.339788
4.52856349955.762998187923.0099925995
3.2229151.7501663008-18.8264465332
3.7428964.329425484512.5241613388
2.79787468911.7319071588-13.1613349915
1.70380.4697028629-16.7725734711
2.06999516492.48305691388.25418
3.63149070745.392830401930.0015144348
3.6099013.58554818723.2453007698
3.9077874.24379720438.938385
3.0739436152.1333828429-11.0077285767
2.5647261.9903374258-6.034776
2.3092832.0211477583-2.004553
2.0453591.7476573384-2.4117052555
1.77402782441.4679709982-2.808121
1.67057728771.5538868894-0.07646142
1.5263150931.3635898576-0.9099388
1.85314834122.22181053577.372601
1.88252520561.91566179552.3786323071
2.85419869423.950229415419.2635
2.8223952.78652098852.2853043079
2.37972235681.8803953482-5.095986
1.96699237821.5014401723-5.0030565262
2.6325353.383255451113.872
2.7760963442.93803103225.2005133629
3.27403163913.835693953611.6829986572
3.4321493.6105026216.102383
4.80956840526.363273432228.0709762573
4.24031972893.5982171661-5.372961
4.8249244695.484348403514.6975336075
2.63518238070.1651915573-34.3444633484
4.39339637766.376631052134.08554
4.3223544.24221943913.1226115227
5.89810037617.675514761932.50879
4.35247755052.6090420034-21.74949646
4.9445225.612337796714.9427709579
3.6528842.1959388994-18.15987
3.6991793.75139895134.480998
2.2330381870.5792569618-22.52667
2.08086633681.9092191481-0.488962
-1.0184029341-4.514324531-53.3578453064
-8.925352-17.8442524211-142.4553222656
-3.44037866592.746575438889.18805
-2.696162-1.85669860149.871923
-4.885533-7.3551052422-41.8589057922
-14.50788-25.3617193248-177.0069122314
IPD Returns
AR-TAR
AR
Figure 1 & 3
IPD ReturnsIPD ReturnsLIBORFT ReturnsGDP GrowthLIB REGFT REGGDP REGFT 1FT2AR-TARTAR-TAR
1986Q411.251.706.25-1.54-0.41-13.33-1.2LIBOR6.25FT1-13.33
1987Q12.442.4410.0018.840.506.25-1.54-0.41-13.33-1.2FT-1.54FT2-1.2
1987Q22.722.729.2515.261.106.25-1.54-0.41-13.33-1.2GDP-0.41
1987Q34.954.9510.385.622.206.25-1.54-0.41-13.33-1.2
1987Q45.625.628.94-32.000.906.25-1.54-0.41-13.33-1.2
1988Q15.205.208.694.051.706.25-1.54-0.41-13.33-1.2
1988Q28.038.039.888.310.506.25-1.54-0.41-13.33-1.2
1988Q37.267.2611.94-0.421.406.25-1.54-0.41-13.33-1.2
1988Q46.696.6913.25-1.020.706.25-1.54-0.41-13.33-1.2
1989Q14.794.7913.0615.840.406.25-1.54-0.41-13.33-1.2
1989Q25.175.1714.253.750.606.25-1.54-0.41-13.33-1.2
1989Q34.214.2114.697.150.106.25-1.54-0.41-13.33-1.2
1989Q41.281.2815.164.060.106.25-1.54-0.41-13.33-1.2
1990Q1-0.09-0.0915.25-6.530.806.25-1.54-0.41-13.33-1.2
1990Q2-2.36-2.3614.976.270.506.25-1.54-0.41-13.33-1.2
1990Q3-2.14-2.1414.97-18.13-1.206.25-1.54-0.41-13.33-1.2
1990Q4-2.03-2.0314.068.15-0.606.25-1.54-0.41-13.33-1.2
1991Q1-1.68-1.6812.4415.46-0.106.25-1.54-0.41-13.33-1.2
1991Q2-0.09-0.0911.31-1.26-0.306.25-1.54-0.41-13.33-1.2
1991Q3-0.05-0.0510.3410.17-0.406.25-1.54-0.41-13.33-1.2
1991Q41.061.0610.94-5.510.106.25-1.54-0.41-13.33-1.2
1992Q10.300.3010.81-0.140.106.25-1.54-0.41-13.33-1.2
1992Q20.390.3910.135.10-0.206.25-1.54-0.41-13.33-1.2
1992Q3-0.82-0.829.000.500.506.25-1.54-0.41-13.33-1.2
1992Q40.050.057.0013.170.606.25-1.54-0.41-13.33-1.2
1993Q10.830.835.944.490.606.25-1.54-0.41-13.33-1.2
1993Q22.492.495.972.620.506.25-1.54-0.41-13.33-1.2
1993Q33.833.836.006.190.906.25-1.54-0.41-13.33-1.2
1993Q47.957.955.3111.740.906.25-1.54-0.41-13.33-1.2
1994Q17.547.545.34-6.431.106.25-1.54-0.41-13.33-1.2
1994Q23.793.795.16-5.551.406.25-1.54-0.41-13.33-1.2
1994Q31.821.825.854.351.406.25-1.54-0.41-13.33-1.2
1994Q41.051.056.561.590.706.25-1.54-0.41-13.33-1.2
1995Q10.910.916.632.370.406.25-1.54-0.41-13.33-1.2
1995Q20.430.436.916.380.506.25-1.54-0.41-13.33-1.2
1995Q30.930.936.787.721.106.25-1.54-0.41-13.33-1.2
1995Q40.880.886.504.890.506.25-1.54-0.41-13.33-1.2
1996Q11.751.756.063.471.006.25-1.54-0.41-13.33-1.2
1996Q22.092.095.781.800.406.25-1.54-0.41-13.33-1.2
1996Q32.082.085.885.990.706.25-1.54-0.41-13.33-1.2
1996Q43.033.036.474.170.806.25-1.54-0.41-13.33-1.2
1997Q12.952.956.315.150.806.25-1.54-0.41-13.33-1.2
1997Q23.443.446.845.050.806.25-1.54-0.41-13.33-1.2
1997Q33.433.437.2512.321.006.25-1.54-0.41-13.33-1.2
1997Q44.534.537.56-1.371.206.25-1.54-0.41-13.33-1.2
1998Q13.223.227.5315.090.806.25-1.54-0.41-13.33-1.2
1998Q23.743.747.81-0.800.706.25-1.54-0.41-13.33-1.2
1998Q32.802.807.31-14.970.906.25-1.54-0.41-13.33-1.2
1998Q41.701.706.1913.571.106.25-1.54-0.41-13.33-1.2
1999Q12.072.075.228.750.506.25-1.54-0.41-13.33-1.2
1999Q23.633.635.132.310.806.25-1.54-0.41-13.33-1.2
1999Q33.613.615.47-3.481.306.25-1.54-0.41-13.33-1.2
1999Q43.913.916.0014.101.106.25-1.54-0.41-13.33-1.2
2000Q13.073.076.22-3.491.106.25-1.54-0.41-13.33-1.2
2000Q22.562.566.16-2.131.006.25-1.54-0.41-13.33-1.2
2000Q32.312.316.130.650.506.25-1.54-0.41-13.33-1.2
2000Q42.052.055.84-1.110.406.25-1.54-0.41-13.33-1.2
2001Q11.771.775.47-8.801.206.25-1.54-0.41-13.33-1.2
2001Q21.671.675.251.190.206.25-1.54-0.41-13.33-1.2
2001Q31.531.534.47-14.560.406.25-1.54-0.41-13.33-1.2
2001Q41.851.854.067.900.306.25-1.54-0.41-13.33-1.2
2002Q11.881.884.162.240.806.25-1.54-0.41-13.33-1.2
2002Q22.852.854.09-11.600.406.25-1.54-0.41-13.33-1.2
2002Q32.822.823.91-21.860.706.25-1.54-0.41-13.33-1.2
2002Q42.382.383.964.580.606.25-1.54-0.41-13.33-1.2
2003Q11.971.973.61-6.520.606.25-1.54-0.41-13.33-1.2
2003Q22.632.633.5913.560.906.25-1.54-0.41-13.33-1.2
2003Q32.782.783.673.820.706.25-1.54-0.41-13.33-1.2
2003Q43.273.273.989.000.906.25-1.54-0.41-13.33-1.2
2004Q13.433.434.330.621.006.25-1.54-0.41-13.33-1.2
2004Q24.814.814.792.170.606.25-1.54-0.41-13.33-1.2
2004Q34.244.244.862.830.106.25-1.54-0.41-13.33-1.2
2004Q44.824.824.846.460.806.25-1.54-0.41-13.33-1.2
2005Q12.642.644.933.000.306.25-1.54-0.41-13.33-1.2
2005Q24.394.394.734.890.706.25-1.54-0.41-13.33-1.2
2005Q34.324.324.557.850.606.25-1.54-0.41-13.33-1.2
2005Q45.905.904.594.180.706.25-1.54-0.41-13.33-1.2
2006Q14.354.354.567.781.106.25-1.54-0.41-13.33-1.2
2006Q24.944.944.73-1.850.406.25-1.54-0.41-13.33-1.2
2006Q33.653.655.053.580.506.25-1.54-0.41-13.33-1.2
2006Q43.703.705.295.970.806.25-1.54-0.41-13.33-1.2
2007Q12.232.235.582.870.706.25-1.54-0.41-13.33-1.2
2007Q22.082.085.984.440.606.25-1.54-0.41-13.33-1.2
2007Q3-1.02-1.026.28-1.780.506.25-1.54-0.41-13.33-1.2
2007Q4-8.93-8.935.95-0.350.506.25-1.54-0.41-13.33-1.2
2008Q1-3.44-3.446.02-10.370.706.25-1.54-0.41-13.33-1.2
2008Q2-2.70-2.705.94-1.46-0.106.25-1.54-0.41-13.33-1.2
2008Q3-4.89-4.896.30-12.99-0.706.25-1.54-0.41-13.33-1.2
2008Q4-14.51-14.512.83-10.74-1.806.25-1.54-0.41-13.33-1.2
Figure 1 & 3
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IPD Returns
Figure 2
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LIBOR
LIB REG
LIBOR Regime
Figure 4
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FT Returns
FT REG
FT Returns Regime
Sheet2
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GDP Growth
GDP REG
GDP Growth Regime
Sheet3
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000
FT Returns
FT 1
FT2
FT Return Regimes (TAR-TAR)
IPD ReturnsAR-TARAR
1986Q4
1987Q12.44
1987Q22.723.047.48
1987Q34.957.4742.57
1987Q45.626.3716.88
1988Q15.204.72-1.92
1988Q28.0311.2255.86
1988Q37.266.40-5.71
1988Q46.696.04-3.04
1989Q14.792.65-27.22
1989Q25.175.6011.64
1989Q34.213.12-12.10
1989Q41.28-2.02-48.11
1990Q1-0.09-1.64-23.25
1990Q2-2.36-4.91-40.63
1990Q3-2.14-1.901.45
1990Q4-2.03-1.90-0.10
1991Q1-1.68-1.284.29
1991Q2-0.091.7126.77
1991Q3-0.05-0.010.55
1991Q41.062.3219.83
1992Q10.30-0.56-12.61
1992Q20.390.481.87
1992Q3-0.82-2.17-21.13
1992Q40.051.0314.73
1993Q10.831.7113.97
1993Q22.494.3630.49
1993Q33.835.3426.47
1993Q47.9512.5977.50
1994Q17.547.080.64
1994Q23.79-0.44-59.56
1994Q31.82-0.39-31.36
1994Q41.050.18-11.98
1995Q10.910.74-1.55
1995Q20.43-0.11-7.59
1995Q30.931.509.39
1995Q40.880.830.07
1996Q11.752.7216.34
1996Q22.092.477.84
1996Q32.082.061.86
1996Q43.034.1019.11
1997Q12.952.851.56
1997Q23.444.0011.78
1997Q33.433.433.34
1997Q44.535.7623.01
1998Q13.221.75-18.83
1998Q23.744.3312.52
1998Q32.801.73-13.16
1998Q41.700.47-16.77
1999Q12.072.488.25
1999Q23.635.3930.00
1999Q33.613.593.25
1999Q43.914.248.94
2000Q13.072.13-11.01
2000Q22.561.99-6.03
2000Q32.312.02-2.00
2000Q42.051.75-2.41
2001Q11.771.47-2.81
2001Q21.671.55-0.08
2001Q31.531.36-0.91
2001Q41.852.227.37
2002Q11.881.922.38
2002Q22.853.9519.26
2002Q32.822.792.29
2002Q42.381.88-5.10
2003Q11.971.50-5.00
2003Q22.633.3813.87
2003Q32.782.945.20
2003Q43.273.8411.68
2004Q13.433.616.10
2004Q24.816.3628.07
2004Q34.243.60-5.37
2004Q44.825.4814.70
2005Q12.640.17-34.34
2005Q24.396.3834.09
2005Q34.324.243.12
2005Q45.907.6832.51
2006Q14.352.61-21.75
2006Q24.945.6114.94
2006Q33.652.20-18.16
2006Q43.703.754.48
2007Q12.230.58-22.53
2007Q22.081.91-0.49
2007Q3-1.02-4.51-53.36
2007Q4-8.93-17.84-142.46
2008Q1-3.442.7589.19
2008Q2-2.70-1.869.87
2008Q3-4.89-7.36-41.86
2008Q4-14.51-25.36-177.01
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000
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000
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000
000
000
000
IPD Returns
AR-TAR
AR
00
00
00
00
00
00
00
00
00
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IPD Returns
AR-TAR
IPD ReturnsTAR-TARARalpha 0.8
1986Q4
1987Q12.44
1987Q22.723.457.483.85
1987Q34.9510.6742.5713.86
1987Q45.627.3316.888.29
1988Q15.20-5.34-1.923.51
1988Q28.0315.3055.8619.36
1988Q37.265.29-5.714.19
1988Q46.695.21-3.044.38
1989Q14.79-0.08-27.22-2.79
1989Q25.176.1611.646.70
1989Q34.211.73-12.100.34
1989Q41.28-6.23-48.11-10.42
1990Q1-0.09-3.61-23.25-5.57
1990Q2-2.36-8.17-40.63-11.42
1990Q3-2.14-1.601.45-1.29
1990Q4-2.030.83-0.10-1.57
1991Q1-1.68-0.774.29-0.26
1991Q2-0.094.0026.776.27
1991Q3-0.050.040.550.09
1991Q41.063.9119.835.51
1992Q10.30-1.66-12.61-2.76
1992Q20.390.611.870.74
1992Q3-0.82-3.91-21.13-5.63
1992Q40.052.2814.733.53
1993Q10.832.8313.973.94
1993Q22.496.7430.499.12
1993Q33.837.2726.479.19
1993Q47.9518.5277.5024.42
1994Q17.546.490.645.90
1994Q23.79-5.84-59.56-11.22
1994Q31.82-3.22-31.36-6.04
1994Q41.05-0.93-11.98-2.04
1995Q10.910.53-1.550.32
1995Q20.43-0.79-7.59-1.47
1995Q30.932.229.392.93
1995Q40.880.760.070.69
1996Q11.753.9716.345.20
1996Q22.092.967.843.45
1996Q32.082.041.862.02
1996Q43.035.4719.116.84
1997Q12.952.741.562.62
1997Q23.444.7111.785.42
1997Q33.433.423.343.41
1997Q44.537.3423.018.91
1998Q13.22-0.13-18.83-2.00
1998Q23.745.0812.525.82
1998Q32.800.37-13.16-0.98
1998Q41.70-25.63-16.77-2.67
1999Q12.073.018.253.53
1999Q23.637.6430.009.88
1999Q33.613.553.253.52
1999Q43.914.678.945.10
2000Q13.070.93-11.01-0.26
2000Q22.561.26-6.030.53
2000Q32.311.65-2.001.29
2000Q42.051.37-2.410.99
2001Q11.771.08-2.810.69
2001Q21.671.41-0.081.26
2001Q31.531.16-0.910.95
2001Q41.8510.027.373.16
2002Q11.881.962.382.00
2002Q22.855.3519.266.74
2002Q32.822.742.292.70
2002Q42.38-8.68-5.100.61
2003Q11.970.91-5.000.32
2003Q22.634.3413.875.29
2003Q32.783.145.203.35
2003Q43.274.5511.685.27
2004Q13.433.846.104.06
2004Q24.818.3428.0710.32
2004Q34.242.78-5.371.96
2004Q44.826.3314.707.16
2005Q12.64-2.99-34.34-6.12
2005Q24.398.9134.0911.43
2005Q34.324.143.124.04
2005Q45.909.9432.5112.20
2006Q14.350.39-21.75-1.83
2006Q24.946.4614.947.31
2006Q33.650.34-18.16-1.51
2006Q43.703.824.483.88
2007Q12.23-1.53-22.53-3.63
2007Q22.081.69-0.491.47
2007Q3-1.02-8.97-53.36-13.42
2007Q4-8.93-29.22-142.46-40.55
2008Q1-3.4410.6489.1918.50
2008Q2-2.70-0.799.870.28
2008Q3-4.89-10.50-41.86-13.64
2008Q4-14.51-39.21-177.01-53.00
2.141.25-1.151.36
3.277.9534.119.82
0.8130.1990.0980.222
-1.999-2.514-2.154-2.721
8.06510.31010.84413.726
IPDTAR TARAR ARAlpha 0.8
IPD1.000
TAR TAR0.7371.000
AR AR0.6180.8891.000
Alpha 0.80.7620.9190.9801.000
2.62
-53.00
24.42
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000
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000
IPD Returns
TAR-TAR
AR
000
000
000
000
000
000
000
000
000
000
000
000
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IPD Returns
TAR-TAR
alpha 0.8
00
00
00
00
00
00
00
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IPD Returns
TAR-TAR
-
AR-TAR versus AR: Fits The AR model appears too volatile particularly across 2008 The AR-TAR model generates more plausible results Still seems rather smoothed Standard deviation compared to IPD 4.8% (3.1%) Serial correlation 0.51 (0.81)
Chart6
2.7249483.0422273209
4.9526476867.4654540165
5.61940240866.3714900883
5.19769763954.7220220266
8.02972611.2242045184
7.2615376.3950332274
6.6858616.0365085284
4.79012632372.6517707251
5.1729775.6048258749
4.20709753043.1176023614
1.2822022438-2.0170285449
-0.08922204-1.6361646749
-2.3555314541-4.9118888834
-2.1429033279-1.903062516
-2.0286085606-1.8996860596
-1.6751872301-1.2765341432
-0.085200851.7082760115
-0.04989183-0.0100638722
1.06174767022.3156576073
0.2975316346-0.5644907036
0.38536563520.4844408535
-0.8175488-2.1744152693
0.051432811.031628886
0.82941471.7069646815
2.48747158054.3577307774
3.8283055.3407416744
7.94688212.5925649092
7.5384467.0777373269
3.7876107693-0.4432658482
1.8224408627-0.3942364628
1.05068171020.1801508681
0.90526120.7412294048
0.4303762-0.1052857843
0.93106041.4958234312
0.88311560.8290347031
1.74748122692.7224705546
2.0883445742.472832475
2.07552838332.061071944
3.02768754964.1017064561
2.9459092.8536642246
3.439779523.9968568393
3.4341895583.4278841785
4.52856349955.7629981879
3.2229151.7501663008
3.7428964.3294254845
2.79787468911.7319071588
1.70380.4697028629
2.06999516492.4830569138
3.63149070745.3928304019
3.6099013.5855481872
3.9077874.2437972043
3.0739436152.1333828429
2.5647261.9903374258
2.3092832.0211477583
2.0453591.7476573384
1.77402782441.4679709982
1.67057728771.5538868894
1.5263150931.3635898576
1.85314834122.2218105357
1.88252520561.9156617955
2.85419869423.9502294154
2.8223952.7865209885
2.37972235681.8803953482
1.96699237821.5014401723
2.6325353.3832554511
2.7760963442.9380310322
3.27403163913.8356939536
3.4321493.610502621
4.80956840526.3632734322
4.24031972893.5982171661
4.8249244695.4843484035
2.63518238070.1651915573
4.39339637766.3766310521
4.3223544.2422194391
5.89810037617.6755147619
4.35247755052.6090420034
4.9445225.6123377967
3.6528842.1959388994
3.6991793.7513989513
2.2330381870.5792569618
2.08086633681.9092191481
-1.0184029341-4.514324531
-8.925352-17.8442524211
-3.44037866592.7465754388
-2.696162-1.8566986014
-4.885533-7.3551052422
-14.50788-25.3617193248
IPD Returns
AR-TAR
Figure 1 & 3
IPD ReturnsIPD ReturnsLIBORFT ReturnsGDP GrowthLIB REGFT REGGDP REGFT 1FT2AR-TARTAR-TAR
1986Q411.251.706.25-1.54-0.41-13.33-1.2LIBOR6.25FT1-13.33
1987Q12.442.4410.0018.840.506.25-1.54-0.41-13.33-1.2FT-1.54FT2-1.2
1987Q22.722.729.2515.261.106.25-1.54-0.41-13.33-1.2GDP-0.41
1987Q34.954.9510.385.622.206.25-1.54-0.41-13.33-1.2
1987Q45.625.628.94-32.000.906.25-1.54-0.41-13.33-1.2
1988Q15.205.208.694.051.706.25-1.54-0.41-13.33-1.2
1988Q28.038.039.888.310.506.25-1.54-0.41-13.33-1.2
1988Q37.267.2611.94-0.421.406.25-1.54-0.41-13.33-1.2
1988Q46.696.6913.25-1.020.706.25-1.54-0.41-13.33-1.2
1989Q14.794.7913.0615.840.406.25-1.54-0.41-13.33-1.2
1989Q25.175.1714.253.750.606.25-1.54-0.41-13.33-1.2
1989Q34.214.2114.697.150.106.25-1.54-0.41-13.33-1.2
1989Q41.281.2815.164.060.106.25-1.54-0.41-13.33-1.2
1990Q1-0.09-0.0915.25-6.530.806.25-1.54-0.41-13.33-1.2
1990Q2-2.36-2.3614.976.270.506.25-1.54-0.41-13.33-1.2
1990Q3-2.14-2.1414.97-18.13-1.206.25-1.54-0.41-13.33-1.2
1990Q4-2.03-2.0314.068.15-0.606.25-1.54-0.41-13.33-1.2
1991Q1-1.68-1.6812.4415.46-0.106.25-1.54-0.41-13.33-1.2
1991Q2-0.09-0.0911.31-1.26-0.306.25-1.54-0.41-13.33-1.2
1991Q3-0.05-0.0510.3410.17-0.406.25-1.54-0.41-13.33-1.2
1991Q41.061.0610.94-5.510.106.25-1.54-0.41-13.33-1.2
1992Q10.300.3010.81-0.140.106.25-1.54-0.41-13.33-1.2
1992Q20.390.3910.135.10-0.206.25-1.54-0.41-13.33-1.2
1992Q3-0.82-0.829.000.500.506.25-1.54-0.41-13.33-1.2
1992Q40.050.057.0013.170.606.25-1.54-0.41-13.33-1.2
1993Q10.830.835.944.490.606.25-1.54-0.41-13.33-1.2
1993Q22.492.495.972.620.506.25-1.54-0.41-13.33-1.2
1993Q33.833.836.006.190.906.25-1.54-0.41-13.33-1.2
1993Q47.957.955.3111.740.906.25-1.54-0.41-13.33-1.2
1994Q17.547.545.34-6.431.106.25-1.54-0.41-13.33-1.2
1994Q23.793.795.16-5.551.406.25-1.54-0.41-13.33-1.2
1994Q31.821.825.854.351.406.25-1.54-0.41-13.33-1.2
1994Q41.051.056.561.590.706.25-1.54-0.41-13.33-1.2
1995Q10.910.916.632.370.406.25-1.54-0.41-13.33-1.2
1995Q20.430.436.916.380.506.25-1.54-0.41-13.33-1.2
1995Q30.930.936.787.721.106.25-1.54-0.41-13.33-1.2
1995Q40.880.886.504.890.506.25-1.54-0.41-13.33-1.2
1996Q11.751.756.063.471.006.25-1.54-0.41-13.33-1.2
1996Q22.092.095.781.800.406.25-1.54-0.41-13.33-1.2
1996Q32.082.085.885.990.706.25-1.54-0.41-13.33-1.2
1996Q43.033.036.474.170.806.25-1.54-0.41-13.33-1.2
1997Q12.952.956.315.150.806.25-1.54-0.41-13.33-1.2
1997Q23.443.446.845.050.806.25-1.54-0.41-13.33-1.2
1997Q33.433.437.2512.321.006.25-1.54-0.41-13.33-1.2
1997Q44.534.537.56-1.371.206.25-1.54-0.41-13.33-1.2
1998Q13.223.227.5315.090.806.25-1.54-0.41-13.33-1.2
1998Q23.743.747.81-0.800.706.25-1.54-0.41-13.33-1.2
1998Q32.802.807.31-14.970.906.25-1.54-0.41-13.33-1.2
1998Q41.701.706.1913.571.106.25-1.54-0.41-13.33-1.2
1999Q12.072.075.228.750.506.25-1.54-0.41-13.33-1.2
1999Q23.633.635.132.310.806.25-1.54-0.41-13.33-1.2
1999Q33.613.615.47-3.481.306.25-1.54-0.41-13.33-1.2
1999Q43.913.916.0014.101.106.25-1.54-0.41-13.33-1.2
2000Q13.073.076.22-3.491.106.25-1.54-0.41-13.33-1.2
2000Q22.562.566.16-2.131.006.25-1.54-0.41-13.33-1.2
2000Q32.312.316.130.650.506.25-1.54-0.41-13.33-1.2
2000Q42.052.055.84-1.110.406.25-1.54-0.41-13.33-1.2
2001Q11.771.775.47-8.801.206.25-1.54-0.41-13.33-1.2
2001Q21.671.675.251.190.206.25-1.54-0.41-13.33-1.2
2001Q31.531.534.47-14.560.406.25-1.54-0.41-13.33-1.2
2001Q41.851.854.067.900.306.25-1.54-0.41-13.33-1.2
2002Q11.881.884.162.240.806.25-1.54-0.41-13.33-1.2
2002Q22.852.854.09-11.600.406.25-1.54-0.41-13.33-1.2
2002Q32.822.823.91-21.860.706.25-1.54-0.41-13.33-1.2
2002Q42.382.383.964.580.606.25-1.54-0.41-13.33-1.2
2003Q11.971.973.61-6.520.606.25-1.54-0.41-13.33-1.2
2003Q22.632.633.5913.560.906.25-1.54-0.41-13.33-1.2
2003Q32.782.783.673.820.706.25-1.54-0.41-13.33-1.2
2003Q43.273.273.989.000.906.25-1.54-0.41-13.33-1.2
2004Q13.433.434.330.621.006.25-1.54-0.41-13.33-1.2
2004Q24.814.814.792.170.606.25-1.54-0.41-13.33-1.2
2004Q34.244.244.862.830.106.25-1.54-0.41-13.33-1.2
2004Q44.824.824.846.460.806.25-1.54-0.41-13.33-1.2
2005Q12.642.644.933.000.306.25-1.54-0.41-13.33-1.2
2005Q24.394.394.734.890.706.25-1.54-0.41-13.33-1.2
2005Q34.324.324.557.850.606.25-1.54-0.41-13.33-1.2
2005Q45.905.904.594.180.706.25-1.54-0.41-13.33-1.2
2006Q14.354.354.567.781.106.25-1.54-0.41-13.33-1.2
2006Q24.944.944.73-1.850.406.25-1.54-0.41-13.33-1.2
2006Q33.653.655.053.580.506.25-1.54-0.41-13.33-1.2
2006Q43.703.705.295.970.806.25-1.54-0.41-13.33-1.2
2007Q12.232.235.582.870.706.25-1.54-0.41-13.33-1.2
2007Q22.082.085.984.440.606.25-1.54-0.41-13.33-1.2
2007Q3-1.02-1.026.28-1.780.506.25-1.54-0.41-13.33-1.2
2007Q4-8.93-8.935.95-0.350.506.25-1.54-0.41-13.33-1.2
2008Q1-3.44-3.446.02-10.370.706.25-1.54-0.41-13.33-1.2
2008Q2-2.70-2.705.94-1.46-0.106.25-1.54-0.41-13.33-1.2
2008Q3-4.89-4.896.30-12.99-0.706.25-1.54-0.41-13.33-1.2
2008Q4-14.51-14.512.83-10.74-1.806.25-1.54-0.41-13.33-1.2
Figure 1 & 3
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IPD Returns
Figure 2
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LIBOR
LIB REG
LIBOR Regime
Figure 4
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FT Returns
FT REG
FT Returns Regime
Sheet2
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GDP Growth
GDP REG
GDP Growth Regime
Sheet3
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FT Returns
FT 1
FT2
FT Return Regimes (TAR-TAR)
IPD ReturnsAR-TARAR
1986Q4
1987Q12.44
1987Q22.723.047.48
1987Q34.957.4742.57
1987Q45.626.3716.88
1988Q15.204.72-1.92
1988Q28.0311.2255.86
1988Q37.266.40-5.71
1988Q46.696.04-3.04
1989Q14.792.65-27.22
1989Q25.175.6011.64
1989Q34.213.12-12.10
1989Q41.28-2.02-48.11
1990Q1-0.09-1.64-23.25
1990Q2-2.36-4.91-40.63
1990Q3-2.14-1.901.45
1990Q4-2.03-1.90-0.10
1991Q1-1.68-1.284.29
1991Q2-0.091.7126.77
1991Q3-0.05-0.010.55
1991Q41.062.3219.83
1992Q10.30-0.56-12.61
1992Q20.390.481.87
1992Q3-0.82-2.17-21.13
1992Q40.051.0314.73
1993Q10.831.7113.97
1993Q22.494.3630.49
1993Q33.835.3426.47
1993Q47.9512.5977.50
1994Q17.547.080.64
1994Q23.79-0.44-59.56
1994Q31.82-0.39-31.36
1994Q41.050.18-11.98
1995Q10.910.74-1.55
1995Q20.43-0.11-7.59
1995Q30.931.509.39
1995Q40.880.830.07
1996Q11.752.7216.34
1996Q22.092.477.84
1996Q32.082.061.86
1996Q43.034.1019.11
1997Q12.952.851.56
1997Q23.444.0011.78
1997Q33.433.433.34
1997Q44.535.7623.01
1998Q13.221.75-18.83
1998Q23.744.3312.52
1998Q32.801.73-13.16
1998Q41.700.47-16.77
1999Q12.072.488.25
1999Q23.635.3930.00
1999Q33.613.593.25
1999Q43.914.248.94
2000Q13.072.13-11.01
2000Q22.561.99-6.03
2000Q32.312.02-2.00
2000Q42.051.75-2.41
2001Q11.771.47-2.81
2001Q21.671.55-0.08
2001Q31.531.36-0.91
2001Q41.852.227.37
2002Q11.881.922.38
2002Q22.853.9519.26
2002Q32.822.792.29
2002Q42.381.88-5.10
2003Q11.971.50-5.00
2003Q22.633.3813.87
2003Q32.782.945.20
2003Q43.273.8411.68
2004Q13.433.616.10
2004Q24.816.3628.07
2004Q34.243.60-5.37
2004Q44.825.4814.70
2005Q12.640.17-34.34
2005Q24.396.3834.09
2005Q34.324.243.12
2005Q45.907.6832.51
2006Q14.352.61-21.75
2006Q24.945.6114.94
2006Q33.652.20-18.16
2006Q43.703.754.48
2007Q12.230.58-22.53
2007Q22.081.91-0.49
2007Q3-1.02-4.51-53.36
2007Q4-8.93-17.84-142.46
2008Q1-3.442.7589.19
2008Q2-2.70-1.869.87
2008Q3-4.89-7.36-41.86
2008Q4-14.51-25.36-177.01
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IPD Returns
AR-TAR
AR
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IPD Returns
AR-TAR
IPD ReturnsTAR-TARARalpha 0.8
1986Q4
1987Q12.44
1987Q22.723.457.483.85
1987Q34.9510.6742.5713.86
1987Q45.627.3316.888.29
1988Q15.20-5.34-1.923.51
1988Q28.0315.3055.8619.36
1988Q37.265.29-5.714.19
1988Q46.695.21-3.044.38
1989Q14.79-0.08-27.22-2.79
1989Q25.176.1611.646.70
1989Q34.211.73-12.100.34
1989Q41.28-6.23-48.11-10.42
1990Q1-0.09-3.61-23.25-5.57
1990Q2-2.36-8.17-40.63-11.42
1990Q3-2.14-1.601.45-1.29
1990Q4-2.030.83-0.10-1.57
1991Q1-1.68-0.774.29-0.26
1991Q2-0.094.0026.776.27
1991Q3-0.050.040.550.09
1991Q41.063.9119.835.51
1992Q10.30-1.66-12.61-2.76
1992Q20.390.611.870.74
1992Q3-0.82-3.91-21.13-5.63
1992Q40.052.2814.733.53
1993Q10.832.8313.973.94
1993Q22.496.7430.499.12
1993Q33.837.2726.479.19
1993Q47.9518.5277.5024.42
1994Q17.546.490.645.90
1994Q23.79-5.84-59.56-11.22
1994Q31.82-3.22-31.36-6.04
1994Q41.05-0.93-11.98-2.04
1995Q10.910.53-1.550.32
1995Q20.43-0.79-7.59-1.47
1995Q30.932.229.392.93
1995Q40.880.760.070.69
1996Q11.753.9716.345.20
1996Q22.092.967.843.45
1996Q32.082.041.862.02
1996Q43.035.4719.116.84
1997Q12.952.741.562.62
1997Q23.444.7111.785.42
1997Q33.433.423.343.41
1997Q44.537.3423.018.91
1998Q13.22-0.13-18.83-2.00
1998Q23.745.0812.525.82
1998Q32.800.37-13.16-0.98
1998Q41.70-25.63-16.77-2.67
1999Q12.073.018.253.53
1999Q23.637.6430.009.88
1999Q33.613.553.253.52
1999Q43.914.678.945.10
2000Q13.070.93-11.01-0.26
2000Q22.561.26-6.030.53
2000Q32.311.65-2.001.29
2000Q42.051.37-2.410.99
2001Q11.771.08-2.810.69
2001Q21.671.41-0.081.26
2001Q31.531.16-0.910.95
2001Q41.8510.027.373.16
2002Q11.881.962.382.00
2002Q22.855.3519.266.74
2002Q32.822.742.292.70
2002Q42.38-8.68-5.100.61
2003Q11.970.91-5.000.32
2003Q22.634.3413.875.29
2003Q32.783.145.203.35
2003Q43.274.5511.685.27
2004Q13.433.846.104.06
2004Q24.818.3428.0710.32
2004Q34.242.78-5.371.96
2004Q44.826.3314.707.16
2005Q12.64-2.99-34.34-6.12
2005Q24.398.9134.0911.43
2005Q34.324.143.124.04
2005Q45.909.9432.5112.20
2006Q14.350.39-21.75-1.83
2006Q24.946.4614.947.31
2006Q33.650.34-18.16-1.51
2006Q43.703.824.483.88
2007Q12.23-1.53-22.53-3.63
2007Q22.081.69-0.491.47
2007Q3-1.02-8.97-53.36-13.42
2007Q4-8.93-29.22-142.46-40.55
2008Q1-3.4410.6489.1918.50
2008Q2-2.70-0.799.870.28
2008Q3-4.89-10.50-41.86-13.64
2008Q4-14.51-39.21-177.01-53.00
2.141.25-1.151.36
3.277.9534.119.82
0.8130.1990.0980.222
-1.999-2.514-2.154-2.721
8.06510.31010.84413.726
IPDTAR TARAR ARAlpha 0.8
IPD1.000
TAR TAR0.7371.000
AR AR0.6180.8891.000
Alpha 0.80.7620.9190.9801.000
2.62
-53.00
24.42
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000
IPD Returns
TAR-TAR
AR
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IPD Returns
TAR-TAR
alpha 0.8
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IPD Returns
TAR-TAR
-
TAR-TAR Model Focus on FT and LIBOR regimes All bar LIBOR-FT models improve SSE Best Model FT-FT All Coefficients Save f1 significant
Model
SSE
TAR
LIBOR-LIBOR
1.42**
(0.28)
0.73**
(0.07)
-0.37
(1.33)
0.79**
(0.14)
3.05**
(0.68)
-0.04
(0.15)
6.21
11.31
0.55
0.00
0.33
0.12
250.3
FT-FT
0.72**
(0.07)
0.96**
(0.04)
3.36**
(0.70)
0.01
(0.09)
-7.13*
(2.61)
1.40**
(0.41)
-13.33
-1.20
0.07
0.00
0.19
0.74
183.2
LIBOR-FT
1.40**
(0.24)
0.56**
(0.09)
1.63**
(0.61)
0.35**
(0.12)
5.28**
(1.61)
-0.85*
(0.42)
6.21
-1.79
0.15
0.40
0.09
0.36
335.9
FT-LIBOR
0.79**
(0.10)
2.22**
(0.80)
0.24
(1.49)
0.59*
(0.29)
3.34**
(1.03)
-0.18
(0.13)
-13.34
5.95
0.02
0.06
0.41
0.51
211.8
AR
0.94**
(0.04)
-1.35
(2.82)
0.12
(0.15)
309.5
_1335081039.unknown
_1335081043.unknown
_1335081045.unknown
_1335081046.unknown
_1335081047.unknown
_1335081044.unknown
_1335081041.unknown
_1335081042.unknown
_1335081040.unknown
_1335081037.unknown
_1335081038.unknown
_1335081036.unknown
-
TAR-TAR (FT Model)Return Processes Differ:FT Returns > -1.2% steady growthFT Returns < -1.2% negative, explosive autoreg.Implies very sharply falling underlying returnsLow regime occurs 26% of timeRegime not persistent Smoothing Processes Differ:FT Returns < -13% very strong smoothingInformation story? This state occurs 7% of time Smoothing parameter lower in other regime
-
TAR-TAR: FT RegimesReturns Regime: C1 = -1.2%Smoothing Regime: C2 = -13.2%
Chart7
18.841917038-13.33-1.2
15.2607927322-13.33-1.2
5.616584-13.33-1.2
-32.0026550293-13.33-1.2
4.0549674034-13.33-1.2
8.310058-13.33-1.2
-0.4158257-13.33-1.2
-1.0190192461-13.33-1.2
15.8391513824-13.33-1.2
3.7536697388-13.33-1.2
7.152185-13.33-1.2
4.0634436607-13.33-1.2
-6.530186-13.33-1.2
6.268623-13.33-1.2
-18.13032341-13.33-1.2
8.147772-13.33-1.2
15.4552135468-13.33-1.2
-1.2575266361-13.33-1.2
10.16984272-13.33-1.2
-5.514645-13.33-1.2
-0.1393856108-13.33-1.2
5.096318-13.33-1.2
0.4986844361-13.33-1.2
13.169506073-13.33-1.2
4.48695-13.33-1.2
2.6163947582-13.33-1.2
6.1890354156-13.33-1.2
11.74033-13.33-1.2
-6.432471-13.33-1.2
-5.54714-13.33-1.2
4.34841-13.33-1.2
1.5851967335-13.33-1.2
2.368151-13.33-1.2
6.381937-13.33-1.2
7.720172-13.33-1.2
4.887479-13.33-1.2
3.473517-13.33-1.2
1.800711-13.33-1.2
5.992757-13.33-1.2
4.1683225632-13.33-1.2
5.147196-13.33-1.2
5.052799-13.33-1.2
12.3165931702-13.33-1.2
-1.3730785847-13.33-1.2
15.0943746567-13.33-1.2
-0.798896-13.33-1.2
-14.9692277908-13.33-1.2
13.5682315826-13.33-1.2
8.746055-13.33-1.2
2.3110244274-13.33-1.2
-3.4791407585-13.33-1.2
14.09605-13.33-1.2
-3.4921572208-13.33-1.2
-2.1302621365-13.33-1.2
0.6456831-13.33-1.2
-1.105868-13.33-1.2
-8.800473-13.33-1.2
1.1919534206-13.33-1.2
-14.55667-13.33-1.2
7.903409481-13.33-1.2
2.2446427345-13.33-1.2
-11.5977525711-13.33-1.2
-21.8640575409-13.33-1.2
4.577512-13.33-1.2
-6.516522-13.33-1.2
13.5642137527-13.33-1.2
3.8169956207-13.33-1.2
8.995739-13.33-1.2
0.6180823445-13.33-1.2
2.171329-13.33-1.2
2.8292126656-13.33-1.2
6.4608635902-13.33-1.2
3.003842-13.33-1.2
4.8901615143-13.33-1.2
7.847241-13.33-1.2
4.178603-13.33-1.2
7.783821-13.33-1.2
-1.8546527624-13.33-1.2
3.5838816166-13.33-1.2
5.97447-13.33-1.2
2.865909338-13.33-1.2
4.441267-13.33-1.2
-1.7781077623-13.33-1.2
-0.3495439-13.33-1.2
-10.37297-13.33-1.2
-1.4569555521-13.33-1.2
-12.993262291-13.33-1.2
-10.742609024-13.33-1.2
FT Returns
FT 1
FT2
FT Return Regimes (TAR-TAR)
Figure 1 & 3
IPD ReturnsIPD ReturnsLIBORFT ReturnsGDP GrowthLIB REGFT REGGDP REGFT 1FT2AR-TARTAR-TAR
1986Q411.251.706.25-1.54-0.41-13.33-1.2LIBOR6.25FT1-13.33
1987Q12.442.4410.0018.840.506.25-1.54-0.41-13.33-1.2FT-1.54FT2-1.2
1987Q22.722.729.2515.261.106.25-1.54-0.41-13.33-1.2GDP-0.41
1987Q34.954.9510.385.622.206.25-1.54-0.41-13.33-1.2
1987Q45.625.628.94-32.000.906.25-1.54-0.41-13.33-1.2
1988Q15.205.208.694.051.706.25-1.54-0.41-13.33-1.2
1988Q28.038.039.888.310.506.25-1.54-0.41-13.33-1.2
1988Q37.267.2611.94-0.421.406.25-1.54-0.41-13.33-1.2
1988Q46.696.6913.25-1.020.706.25-1.54-0.41-13.33-1.2
1989Q14.794.7913.0615.840.406.25-1.54-0.41-13.33-1.2
1989Q25.175.1714.253.750.606.25-1.54-0.41-13.33-1.2
1989Q34.214.2114.697.150.106.25-1.54-0.41-13.33-1.2
1989Q41.281.2815.164.060.106.25-1.54-0.41-13.33-1.2
1990Q1-0.09-0.0915.25-6.530.806.25-1.54-0.41-13.33-1.2
1990Q2-2.36-2.3614.976.270.506.25-1.54-0.41-13.33-1.2
1990Q3-2.14-2.1414.97-18.13-1.206.25-1.54-0.41-13.33-1.2
1990Q4-2.03-2.0314.068.15-0.606.25-1.54-0.41-13.33-1.2
1991Q1-1.68-1.6812.4415.46-0.106.25-1.54-0.41-13.33-1.2
1991Q2-0.09-0.0911.31-1.26-0.306.25-1.54-0.41-13.33-1.2
1991Q3-0.05-0.0510.3410.17-0.406.25-1.54-0.41-13.33-1.2
1991Q41.061.0610.94-5.510.106.25-1.54-0.41-13.33-1.2
1992Q10.300.3010.81-0.140.106.25-1.54-0.41-13.33-1.2
1992Q20.390.3910.135.10-0.206.25-1.54-0.41-13.33-1.2
1992Q3