comparison of forecasting methods for agriculture

8/6/2019 Comparison of Forecasting Methods for Agriculture

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Comparison of forecasting methods for agriculture

IEM, MED, NIT Calicut Page 1

CHATPTER 1

1. Introduction

The field of forecasting is concerned with making statements about matters that are currently

unknown. The terms forecast, prediction, projection, and prognosis are

interchangeable as commonly used. Forecasting is also concerned with the effective

presentation and use of forecasts. Useful knowledge comes from empirical comparisons of

alternatives and this entry is concerned primarily with evidence-based or scientific

procedures. Before forecasting, one should consider whether it is necessary. Forecasting is

needed only if there is uncertainty; a forecast that the tide will turn is of no value. Forecasts

are also unnecessary when one can control events. Forecasting should not be confused with

planning. Whereas planning is concerned with what the planner thinks the future should be

like, forecasting is concerned with what it will be like. Managers should start by planning.

Forecasting procedures are then used to predict outcomes for the plans. If the managers do

not like the forecasts, the planning and forecasting processes can be repeated until a plan is

found that leads to forecasts of acceptable outcomes. The best plan can then be implemented

and actual outcomes monitored so that the feedback can be used in the next planning period.

The Methodology Tree for Forecasting (Figure 1) is a classification schema of all forecasting

methods organized on the basis of the source of the knowledge the forecaster has about the

situation. Some methods use primarily judgmental or qualitative knowledge while others

require statistical data. There is an increasing integration in the use of judgment and statistics

in the procedures as one follows the Tree down.

The most common way to make forecasts is to ask experts to think about a situation and

predict what will happen. If experts forecasts are derived in an unstructured way the

approach is referred to as unaided judgment. It is fast, can be inexpensive when few forecasts

are needed, and can be appropriate when small changes are expected. It is most likely to be

useful when the forecaster knows the situation well, makes frequent forecasts, and gets good

feedback about the accuracy of his forecasts, as is the case with short-term weather

forecasting and sports betting.

Expert forecasting refers to combining forecasts obtained from experts using validated

structured techniques. Which method is most appropriate depends on time constraints,dispersal of knowledge, access to experts, expert motivation, and need for confidentiality. To


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The structured analogies method uses information about similar situations to obtain

forecasts. Experts identify situations that are analogous to a target situation, describe

similarities and differences to the target, and then derive an overall similarity rating. The

outcome or decision implied by each experts top-rated analogy is the structured analogies

forecast from that expert.

Judgmental bootstrappingis a method for deriving a forecasting model by regressing experts

forecasts against the information the experts used to make their forecasts. The method is

useful when expert judgments have predictive validity but data are scarce (e.g., forecasting

new products) and outcomes are difficult to observe (e.g., predicting performance of

executives). Once developed, judgmental bootstrapping models are a low-cost forecasting

method. A meta-analysis found judgmental bootstrapping to be more accurate than unaided

judgment in 8 of 11 comparisons. Two tests found no difference, and one found a small loss

in accuracy. The typical error reduction was about 6%

Expert systemsare forecasting rules derived from the reasoning experts use when they make

forecasts. They can be developed using knowledge from diverse sources such as surveys,

interviews of experts, or protocol analysis in which the expert explains what he is doing as he

makes forecasts. A meta-analysis on the predictive validity of the method found that expert

systems were more accurate than unaided judgment in six comparisons, similar in one, and

less accurate in another. Expert systems were less accurate than judgmental bootstrapping in

two comparisons and similar in two.

Role playing involves asking people to think and behave in ways that are consistent with a

role and situation described to them. Role playing for the purpose of predicting the behaviour

of people who are interacting with each other is called simulated interaction. The decisions

made in the simulated interactions are used as forecasts of

the actual decision.

Conjoint analysis is a method for eliciting peoples preferences for different possible

offerings (e.g. for alternative mobile phone designs or for different political platforms) by

exposing people to several combinations of features (e.g. weight, price, and screen size of a

mobile phone.) The possibilities can be set up as experiments where variations in each


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variable are unrelated to variations in other variables. Regression-like analyses are then used

in order to predict the combination of features that people will find most desirable.


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CHAPTER 2

2. Importance of agricultural forecasting.

Economic forecasting in agriculture has some features in common with business forecasting

and with macroeconomic forecasting. But over time, it has developed a focus of its own.

During the second quarter century, the profession shifted toward prediction, broadly defined,

including use of econometric techniques for estimating elasticities and forecasting prices. The

third quarter century, from 1975 onwards, has been characterized by research on policy, trade

and the global economy and expansion to environmental and resource problems. Throughout

the entire period, and more markedly of late, explanation of past behaviour has been the

dominant focus of agricultural supply modelling, which is the area to which most agricultural

forecasting belongs.

Because an assured food supply is important to national security, governments have

attempted to quantify agricultural production and to exert some control over it. In the

beginning, simply collecting and tabulating data on the current agricultural situation was a

major challenge, and agricultural statisticians played a major role in the development of

statistical methods. Data revision was frequent. Estimates of production, for example, were

subject to revision after a new census had been tabulated. The large number of Situation

reports or similarly titled publications indicates the fascination of agricultural statisticians

with estimating the current status of a data series.

The nature of agricultural production and the historical relations among the different groups

of participants in agriculture make agriculture different from most economic activity. Most

product is unbranded and sold in markets where individual suppliers have no say in price

determination. Both nature and government policy can have a major impact on a farmers

production and profits. Farmers and others connected with agriculture are used to receiving

technical and economic information from publicly supported institutions.

2.1. Characteristics of agricultural production

Agricultural production is unusual compared with most business activity in its strong

dependence on biological processes. Farmers have minimal ability to alter the rate of

development of a crop or animal. Second, for most commodities, the production cycle is

measured in months or years. Other features impose dynamic structure, especially on prices:


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seasonal impacts on production, high cost of adjustment once production is underway and the

need to carry inventory. Estimation of leading indicators therefore became a major part of

short-term agricultural production forecasting, dominating any work on price forecasting. The

estimation of leading indicators was a natural extension of the data gathering activity

concerning current production or inventories. For example, estimation of acres planted to

spring wheat is a good indication of harvested acreage. In no other sector has leading

indicator analysis found such long-term and widespread use.

Agricultural production appears to meet the four conditions laid down for good forecasts by

econometric methods there should be strong causal relationships, relations should be capable

of being measured accurately, causal variables should change substantially and it should be

possible to forecast changes in causal variables. Unfortunately, econometric methods do

poorly at forecasting agricultural production and prices. The most likely reason is the great

influence on production of random shocks. Relative to most manufacturing activity,

agriculture is greatly influenced by unpredictable random events such as droughts, hoods and

attacks by pests. The consequence of these shocks on production can be assessed reasonably

well after they have occurred, which is useful in making post-harvest production estimates,

but not pre-harvest forecasts.

2.2Producers of agricultural forecastsThe predominant forecaster of production, prices and trade of agricultural commodities and

inputs in most countries is central government. The Economic Research Service of the United

States Department of Agriculture (USDA-ERS) contains the largest agglomeration of

agricultural economists and produces the greatest number of agricultural forecasts.

Government commodity specialists are the main providers of outlook information in

Australia, Canada and the US. Reports on the situation and outlook for commodity and input

markets at local, national and world levels are issued from one to twelve times a year

depending on commodity and country. Some agencies issue regular medium-term forecasts

(2-5 years ahead). For example, Agriculture Canada has issued Long-term projections are

generally issued only irregularly, and usually for groups of commodities. Although

governments publish many forecasts, often as regular series, they also make many forecasts

solely for internal use, for example, the USDA forecasts of the budgetary cost of the farm

program medium-term outlook reports twice a year since.


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Other public agencies, from the Food and Agricultural Organization of the United Nations to

regional or provincial governments, also produce forecasts. University faculty and (in the US)

extension economists prepare forecasts for general release as part of short-term outlook

programs for local farmers and agribusinesses. They may also present forecasts in scholarly

publications; these usually have a methodological focus.

Private companies that process or trade commodities or supply inputs produce forecasts for

in-house use, typically with relatively simple models combined with judgment. They are

probably closest to business forecasters in both approach and objectives. Private consultants

also produce forecasts for sale, most frequently as adjuncts to large-scale macroeconomic

models. Farmers practically never produce formal forecasts, though most of them doubtlessly

form a judgment about future outcomes of their business choices.

2.3Users of agricultural forecastsFarmers may rarely make forecasts, but they form the largest group of users. They need to

make production and marketing decisions that may have financial repercussions many

months in the future. Short-run commodity outlook forecasts, at least in the US, have tended

to emphasize production and inventory information. Farmers have more use for price

forecasts. Once committed to a product, farmers are price takers. They produce goods that are

homogeneous or highly substitutable with the goods of their competitors, who may either be

their neighbours or live halfway round the world. They have no concern with problems

common in manufacturing, such as the amount of sales of a branded product or what quantity

of a specific model to keep in inventory. But farmers, especially those in developed countries,

must also be concerned with the ways in which changes in government policy will alter their

business conditions. Agricultural journalists represent a second kind of audience for

commodity forecasts. They are not users in the sense of being makers of decisions based on

forecast information. They provide an indirect way for readers and listeners (mainly farmers)

to receive outlook forecasts. Processors of food and fibre, and others in the marketing chain,

need forecasts to aid in their purchasing and storing decisions. They too would probably like

price forecasts, but would be able to make greater use of production forecasts in their

decisions than would farmers. Larger businesses also supplement public forecasts with their

own in-house ones.


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Governments in many countries intervene in agricultural production to protect domestic

agriculture and provide food security. For this they need two kinds of information. First, for

legislation and, to a much lesser extent, for program implementation, governments need to

know the consequences of different policy choices on different groups in society.

Agricultural economists have been especially willing, over the last 30 years, to build ever

larger models to provide answers to policy questions. Emphasis has been placed on

comparing proposed policies via simulations, which has measurably assisted legislators.

Forecasts of output and prices are conditional on the policy actually selected. To date, efforts

to forecast which policy will be selected have been minimal.

Neither have government or academic economists done much to evaluate a models ability to

forecast the actual consequences of an adopted policy. Second, in monitoring the progress of

farm programs designed to control supplies or support prices, governments would like to

know about the effectiveness of the program and anticipated budget outlays.


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CHAPTER 3

3. Data collection for analysis

Agricultural data is not very difficult to obtain. But, getting the authentic data was very

important for our analysis. Data from different sources were collected, sorted, analysed and

finally we had narrowed down our search to the data published by the central government of

India, Ministry of Agriculture. The data we collected consisted of the past history of the

produce of about 25 crops over a span of 25 years from 1984 to 2008. After further analysing

the data we selected 10 crops for the further analysis. The selection of the data was purely

based on the fact that some of the crops did not have a consistent set of data ie. for some

crops the data over the years were not present.

The data analysis part consisted of two main parts. First, it was to study the property of the

data. For the given model the data was assumed to follow the first order auto-correlation. The

stage consisted of determining the parameters required for the forecasting models and to

forecast one period into future and compare the models. For the comparison we have selected

three models. Firstly, Exponentially Weighted Moving Average, secondly, Trend Adjusted

moving Average and finally, the Mean Square Optimal method.

The parameters required for each was determined using either analytical of by using

simulation. The data collected is being tabulated in the table below.


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Table 1: Agricultural data over past 25 years (in mega tonnes)

crop rice sugarcane wheat milk vegetables potato millet maize groundnuts coconut

year

1984 17427944 3380547 6447852 11850637 4128300 1565582 1601937 894614 2869123 4645171985 19081147 3307590 6248398 12587400 4203360 1627722 1203988 704062 2238634 454913

1986 18314686 3334036 6671234 18314686 4447305 1318852 1360891 804661 2607717 428504

1987 17013045 3613848 6284262 12898588 4503600 1642566 1117846 606250 2540184 488556

1988 21171447 3820620 6546232 13206280 4334715 1820911 1828702 872046 4372493 573932

1989 21969341 3942964 7672064 14195790 4184595 1936852 1733080 1022827 3633177 628919

1990 22597604 4380542 7305245 14513971 4240890 1925393 1681365 899817 3338196 653881

1991 22721384 4681091 8087016 14323162 4334715 1942138 1317172 721416 3152164 678300

1992 22074476 4932660 8195579 14785200 3865590 2351405 1974488 848155 3857443 755264

199324449500 4428327 8424183 15407577 4147065 2437367 1374719 713468 3518262 804373

1994 24917312 4460179 8820980 16247236 4053240 2274581 1657749 611955 3641368 893719

1995 23404729 5350972 9745848 17917065 3788653 2266681 1384728 655484 3405527 870274

1996 24877437 5458947 9165961 18751729 3753000 2443399 1769808 787138 3936811 877268

1997 25106636 5390201 10271064 19334646 3753000 3231954 1676829 783885 3311295 813055

1998 26218740 5428681 9795029 20186293 4240890 2263357 1656078 821034 4107969 791350

1999 27361764 6026647 10557335 21112866 5072179 2951660 1391515 840428 2840428 780497

2000 25890853 5781769 11367806 21692286 5372419 3345146 1626972 873731 2920525 755174

2001 28546322 5716715 10327497 22678299 6631551 2933998 1832010 979589 3195190 784114

2002 21808324 5740895 10820910 23232744 5100327 3237019 1020485 771997 3771997 806724

2003 27050186 5551122 9719472 23965510 6518961 3014991 2394778 1181440 3702426 780497

2004 25332886 4517297 10708479 25063911 3597757 3696970 1756474 1073339 3045803 757887

2005 28042829 4604244 10164358 26008965 4151512 3811475 1703087 1120272 3672741 798494

2006 28341887 5460342 10251551 27163809 5156772 3827306 1676096 1139224 4113922 921583

2007 29476025 6904174 11245019 27928543 5469246 3731788 2064876 1550386 4226948 985253

2008 30246312 6725632 11671546 30419550 5892585 4602900 1841508 1442042 4144204 985253


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CHAPTER 4

4. Study of properties of data

Suppose we have a time series regression model relating a "dependent" time series {yt} to

the independent" time series {x1t}, . . . , {xpt}. The model is

where {t} is a time series of "errors", or "disturbances". Such models are useful for both

explanatory and forecasting purposes. The parameters 0 , 1, . . . , t may be estimated by

least-squares. In practice, it often happens that the errors are not independent (as assumed instandard regression models) but instead are autocorrelated. Such error autocorrelation, or

"serial correlation", has many undesirable but correctable consequences (e.g., the least-

squares estimates sub-optimal, standard confidence intervals for are incorrect, the error

term is forecastable). Thus, it is highly desirable to try to detect error autocorrelations.

The Durbin-Watson Test for serial correlation assumes that the t are stationary and

normally distributed with mean zero. It tests the null hypothesis H0 that the errors are

uncorrelated against the alternative hypothesis H1 that the errors are AR (1). Thus, ifs are

the error autocorrelations, then weH0 =0 (s > 0), andH1 = s=sfor some nonzero with || 0, || < 1, and {t} is an independent and

identically distributed normal (IIDN) process with mean 0 and variance 2

e. The condition of |

| < 1 ensures that the process is stationary. It is useful to note that

=

1

and

=

( 1 )


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In practice, if is unknown, we may first obtain unbiased estimates of demand parameter, ,

and then substitute the demand parameter with the corresponding parameter estimate.

As noted earlier, the AR(1) model is widely used in supply-chain management research (e.g.,

Chen, Ryan, & Simchi-Levi, 2000b; Lee, So, & Tang, 2000). One of the primary reasons for

the focus on the AR(1) model isthat it possesses good dynamic characteristics. Namely, by

varying the parameter, we are able to study the effects of processes which are random,

nonrandom but stationary or even nonstationary processes. This flexibilityallows us to gain

practical insights for many real demand patterns.

By varying the values of, one can represent a wide variety of process behaviours. When =

0, we have an IIDN process with mean s and variance . For _1 < < 0, the process is

negatively correlated and will exhibit period-to-period oscillatory behaviour. For 0 < < 1,

the demand process will be positively correlated which is reflected by as wandering or

meandering sequence of observations. As approaches | |1, the process approaches

nonstationary behaviour, most notably, the random walk model ARIMA(0,1, 0) is a

special case of the AR(1) model when = 1. As pointed out by Graves and Willems (2000),

varying a stationary demand model is an important exercise for gaining fundamental insights

into the relationship between variables such as inventory and orders relative to demand

characterization.

Forecast models

Smoothing methods, such as moving averages and exponential smoothing are widely

employed for forecasting purposes in many production and operations management

applications, largely because of their simplicity and ease of implementation. As such, most

researchers of supply-chain management (SCM) problem requiring a forecast model have

based their studies on either the moving-average method (e.g., Chen et al., 2000a) or the

exponential weighted moving-average (EWMA) method (e.g., Chen et al., 2000b). Given the

close connection between the moving-average method and the EWMA method, we will only

focus on one method (namely, the EWMA method) in this paper.

The EWMA model can be expressed as follows:

Ft+1|t = dt + (1- ) Ft|t-1


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where 0 < < 1 is the smoothing constant and Ft+1jt is the forecast of period t + 1 made at

the end of period t. It should be noted that the forecasts for periods t + i (i = 1,2,. . .) made at

time t are equal, that is, Ft+i|t = Ft+1|t for i = 1,2,. . .. Hence, the forecasts for all lead times will

follow a horizontal line parallel to the time axis.

Even though the EWMA method, and to a lesser extent the moving-average method, has

flexibility for adapting to a variety of correlated demand processes, it is MSE optimal for

only one underlying time-series model, namely, a first-order integrated moving average,

denoted by ARIMA(0, 1, 1) or IMA(1, 1) (e.g., Graves, 1999). An ARIMA (0, 1, 1) process

is a nonstationary process that can be interpreted as a random walk trend plus a random

deviation from the trend. Thus, under no circumstance is the EWMA method MSE optimal

for a stationary AR(1) process. This fact opens up consideration of employing an MSE-

optimal forecast scheme for the assumed AR(1) process.

By recursively applying (1), it is easy to show that:

(2)

For a general ARIMA process, it can be shown that the minimum mean square error forecast

for period t + i is the conditional expectation of d t+i given current and previous observations

dt, dt-1, dt-2,. . . (see Box, Jenkins, & Reinsel, 1994). In the case of an AR(1) process, this

implies the MSE-optimal forecast function is given by E(dt+i|dt). Since E(t+i|dt) = 0 for i =

1,2,. . ., it immediately follows that for an AR(1) process, the MSE-optimal forecast function

is given by:

|

=1

1 +

In contrast to the two previous methods, this forecast function is not a horizontal projection

into the future. Instead the forecasts revert back towards the overall mean level of /1-. The

MSE-optimal forecast function reflects the fact that the AR(1) process is stationary and has

the property of conditional mean reversion; that is, even though the process can be expected

to wander away (below or above) from the overall mean it is also expected to eventually

return back to the overall mean. The moving-average and EWMA methods fail to capture this

mean reversion property of a stationary AR(1) process.


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One argument often presented against the use of optimal methods is that their implementation

is more difficult than the simple smoothing methods when parameters are unknown. It is

pointed out that to implement optimal methods requires statistical skills in time-series

modelling, including knowledge of model identification, model estimation, and tests for

model adequacy, that are beyond the skill set of a typical operations manager. However, we

believe that the industrial use of more sophisticated time-series models is steadily growing

because of two reasons. First, the requirement of intense statistical training, often referred to

as 6 training, is increasingly becoming commonplace (Hoerl, 1998). At corporations like

GE, Motorola, and Allied Signal, organizational cultures are being developed in which there

is a strong desire from employees throughout the organization to learn and implement

advanced statistical techniques. Indeed, the authors of this paper can report that seminars in

time-series analysis are part of the regular continuing education program at GE-Medical

Systems and are required to be taken by all supply-chain managers. Second, modern

computational tools are readily available to make possible automated implementation of

time-series modelling including the general class of ARIMA models. These programs are

designed to automate model identification, model fitting, and forecasting.


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CHAPTER 5

5. Analysis done on each data set

Each data set was carefully analysed and the above mentioned properties were checked for.

The data collected for each crop or the yield of each crop over the last 25 years had the

characteristics that were required for the model to be applied and tested. All analysis done on

each data set is being listed below and some of them are being explained in detail.

Check for Auto-Correlation.

Calculation of.

Calculation of the optimal period for moving average

Calculation of.

Calculation of the errors.

Checking the normal behavior of the errors.

Forecasting using both models.

Comparison of the results.

Calculation of and

As we have already mentioned above that the demand is assumed to follow the first orderautocorrelation. In a first order auto correlated demand, the demand is being related to the

previous year demand as given by the equation:

When we closely observe the relationship, we can see that this follows a regression, where

the independent variable is the present demand and the dependent variable is the previous

period demand. Thus, applying the basic concept in the determination of the parameters for

the regression analysis, we assume that for the best fit line the error is zero. This leaves us

with the equation for the straight line. For this straight line we can see that the slope of the

line, in this case which is given by can be calculated using the equation

= ( )

( )


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Where d is the two period moving average. Here we have taken the two period moving

average other than the average over the period, since with two period moving average we

have found that the error in the forecasting was comparatively lesser than that with the

average over that entire data. On further thought why is this phenomenon being observed

we concluded that this could be attributed to the reverting property of the AR(1) models.

This property tends to bring the forecast closer to the mean. But for a positively correlated

data this leads to a large error. This drawback can be solved by going for a moving

average. The period for the moving average was determined using spreadsheet

simulation, where 2,3,4 and 5 period moving average was tested. It was surprisingly

found that for all data sets 2 period moving average yielded the best results.

This can be explained by the fact that the factors affecting the agriculture do not change

abruptly. They follow a gradual change. The changes could be technological, physical

(government policies) or even natural. Thus the forecast yielded best results with 2 period

moving average. Statistically speaking, the data showed large amount of first order

autocorrelation. And for higher orders it became less significant.


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CHAPTER 6

6. Results

The above analysis will be explained with the help of a single data set. This data set that wehave selected is for rice and paddy. The test static obtained for Durbin-Watson test was

1.964. since the value is less than 2 the data can be said to be first order auto correlated. The

value of was obtained to be 0.965 and as 0.915. The normality of the error was analysed

with the help of the statistical packages like SPSS and Minitab. The mean and standard

deviation was found to be 7.2 x 10-16

and 0.978. this shows that the mean is almost zero and

the normality of the error was checked with the help of the probability value and the normal

probability plot. The p value was found to be 0.583. Since the probability value is less than

the value of critical value of 0.05 at 95% confidence level the hypothesis that the error

follows the normal distribution can be accepted. The plots are being shown below.

3210-1-2-3

99

95

90

80

70

60

50

40

30

20

10

5

1

C1

Percent

Mean 0.0000004167

StDev 0.9780

N 24

AD 0.290

P -V alu e 0.583

Probability Plot of C1Normal

Figure 2 : Histogram and normal probability plot for rice and paddy

The fore casting using the two methods has been shown in the table given below. It can

be seen that MSE optimal gives the better forecast for the agricultural yield.


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Table 2: Forecast results for rice and paddy

year procduction

in MT

moving

avg

=(1-) forecast

using MSE

error in

forecast

for MSE

forecast

using

EWMA

error in

forecast

for

EWMA

1984 17427944 0.9653 633370

1985 19081147 18254546 0.9653 634065 17456624 2.6E+12 1.6E+07 9.8E+12

1986 18314686 18274592 0.9653 623123 19026149 5.1E+11 1.9E+07 2.5E+11

1987 17013045 17959206 0.9653 645413 18278953 1.6E+12 1.8E+07 1.8E+12

1988 21171447 18601654 0.9653 664888 17222310 1.6E+13 1.7E+07 1.6E+13

1989 21969341 19162935 0.9653 681912 20846360 1.3E+12 2.1E+07 1.3E+12

1990 22597604 19653602 0.9653 695217 21527184 1.1E+12 2.2E+07 5.3E+11

1991 22721384 20037075 0.9653 703072 22036830 4.7E+11 2.3E+07 3.4E+10

1992 22074476 20263453 0.9653 717596 22116475 1.8E+09 2.3E+07 4E+111993 24449500 20682057 0.9653 730955 21695373 7.6E+12 2.2E+07 5.4E+12

1994 24917312 21067081 0.9653 737714 23443188 2.2E+12 2.4E+07 4.4E+11

1995 23404729 21261885 0.9653 747364 23740679 1.1E+11 2.5E+07 2.1E+12

1996 24877437 21540004 0.9653 756203 22760626 4.5E+12 2.4E+07 1.8E+12

1997 25106636 21794763 0.9653 766436 23742623 1.9E+12 2.5E+07 1.2E+11

1998 26218740 22089695 0.9653 777869 23929877 5.2E+12 2.5E+07 1.3E+12

1999 27361764 22419200 0.9653 784955 24656318 7.3E+12 2.6E+07 1.5E+12

2000 25890853 22623414 0.9653 796371 25316492 3.3E+11 2.7E+07 1.9E+12

2001 28546322 22952465 0.9653 794282 24564575 1.6E+13 2.6E+07 6.4E+12

2002 21808324 22892247 0.9653 801495 25886655 1.7E+13 2.8E+07 4.3E+13

2003 27050186 23100144 0.9653 805184 22439731 2.1E+13 2.2E+07 2.2E+13

2004 25332886 23206465 0.9653 812812 25103297 5.3E+10 2.7E+07 1.7E+12

2005 28042829 23426300 0.9653 820227 24334533 1.4E+13 2.5E+07 6.7E+12

2006 28341887 23640021 0.9653 828664 25664599 7.2E+12 2.8E+07 2.7E+11

2007 29476025 23883188 0.9653 837495 25862329 1.3E+13 2.8E+07 1.4E+12

2008 30246312 24137713 26425083 1.5E+13 2.9E+07 7.6E+11

mean

square

error

5.4E+12 6.3E+12

The results of the analysis on the other crops are given in the table below.


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Table 3: Results for the forecasting of other crops

From the table it can be seen that the buffalo milk, sugarcane and the vegetables do have the

errors which follow the normal distribution. In this case the basic assumption is being

violated and so the data do not follow the demand distribution equation. Thus they have to be

considered separately and the other forecasting techniques should be used for their prediction.

crop durbin-

watson

test static

error in

forecast for

MSE

error in

forecast for

EWMA

p- value for

the error

rice and paddy 1.964 0.965 0.915 5.446E+12 6.3E+12 0.583

sugarcane 0.764 0.961 0.904 1.405E+11 2.6E+11 0.005

wheat 0.569 0.977 0.915 2.58E+12 3E+12 0.139

buffalo milk 0.814 0.930 0.833 2.577E+12 3.8E+12 0.005

vegetables 1.138 0.968 0.923 4.429E+11 7E+11 0.02

potato 1.001 0.906 0.778 6.922E+10 1.6E+11 0.305

millet 1.132 0.967 0.919 1.487E+11 2E+11 0.457

maize 1.389 0.938 0.852 1.621E+10 2.6E+10 0.148

groundnuts 1.556 0.974 0.936 3.21E+11 3.7E+11 0.707

coconut 0.939 0.957 0.896 1.663E+09 2.9E+09 0.648


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Figure 3 : Histogram and normal probability plot for sugarcane

Figure 4 : Histogram and normal probability plot for wheat


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Figure 5 : Histogram and normal probability plot for milk

Figure 6 : Histogram and normal probability plot for vegetables


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Figure 7 : Histogram and normal probability plot for potato

Figure 8 : Histogram and normal probability plot for millet


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Figure 9 : Histogram and normal probability plot for maize

Figure 10 : Histogram and normal probability plot for groundnut


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Figure 10 : Histogram and normal probability plot for coconut


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CHAPTER 7

Conclusion

In this research, we found that in most of the cases the agricultural yield tends to follow the

first order auto correlation. This property was tried to exploit and by using MSE optimal

forecasting model the agricultural produce for next period was tried to be forecasted. The

MSE optimal model was compared to the exponential weighted mean average method of

forecasting and it was found that the MSE optimal was gave a better estimate. The

performance parameter that was taken for comparison was the mean square error. The MSE

optimal method gave forecasts with lesser amount of mean square error.

The normality of the errors were also studied and expect for a few all other gave the resultsthat the errors were normally distributed and they had a mean of zero. In practice though the

mean was not actually zero but the value was small enough to be approximated to zero.

In this research we had restricted ourselves to the analysis were we tried to capture only the

effect of the previous year yield. But in actual practice it is not so. Agriculture depends upon

a lot of factors such as weather, new technological development, new variety of seeds,

government policies, etc. since some of the factors which affect the agriculture are not

quantitative it becomes all the more difficult to capture their effect. However this opens a

wide area for future research.


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comparison of forecasting methods for agriculture

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