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Page 1: Ch1. Introduction - people.missouristate.edupeople.missouristate.edu/songfengzheng/Teaching/MTH548/Time Series... · Time Series Analysis Ch1. Introduction. 1.3. Time Series Plot

Ch1. Introduction

Time Series Analysis

Time Series Analysis Ch1. Introduction

Page 2: Ch1. Introduction - people.missouristate.edupeople.missouristate.edu/songfengzheng/Teaching/MTH548/Time Series... · Time Series Analysis Ch1. Introduction. 1.3. Time Series Plot

Introduction

A time series is a sequence of data points, measured typically atsuccessive points in time spaced at uniform time intervals (wiki).For examples:

The daily closing price of a stock.

The daily outside temperature of Parker Hall at noon.

The quarterly economic data (say, GDP, CPI, unemploymentrate, etc.)

The population of wild rabbits in a region.

An observed time series is often modeled by a sequence of randomvariables (i.e. a stochastic process) {Yt : t = 0,±1,±2,±3, · · · }.We will use a free statistical software, R, to analyze and modeltime series. (See the handout “An Introduction to R”.)

Time Series Analysis Ch1. Introduction

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1.1 Examples of Time Series

Time Series Analysis Ch1. Introduction

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chap1.R:

Exhibit 1.3: Time Series Plot of Color Property from a Chemical Process

Exhibit 1.4: Scatterplot of Color Value versus Previous Color Value

Time Series Analysis Ch1. Introduction

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chap1.R:

Exhibit 1.5: Abundance of Canadian Hare

Exhibit 1.6: Hare Abundance versus Previous Years Hare Abundance

Time Series Analysis Ch1. Introduction

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chap1.R:

1.7: Average Monthly Temperatures, Dubuque, Iowa [Seasonality]

Time Series Analysis Ch1. Introduction

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chap1.R:

1.8: Monthly Oil Filter Sales

1.9: Monthly Oil Filter Sales with Special Plotting Symbols

Time Series Analysis Ch1. Introduction

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1.2. A Model-Building Strategy

Three main steps (Box & Jenkins 1976):

1 model identification: Choose appropriate classes of time series models for a given

observed series. In this step we look at the time plot of the series, compute many different statistics from

the data, and also apply any knowledge of the subject matter in which the data arise, such as biology,

business, or ecology. The model chosen at this point is tentative and subject to revision later on in the

analysis.

The principle of parsimony:

models should be simple, but not too simple.

2 model fitting: Model fitting consists of finding the best possible estimates of those unknown

parameters within a given model. We shall consider criteria such as least squares and maximum likelihood

for estimation.

3 model diagnostics: How well does the model fit the data? Are the assumptions of the

model reasonably well satisfied? If no inadequacies are found, the modeling may be assumed to be

complete, and the model may be used, for example, to forecast future values.

Time Series Analysis Ch1. Introduction

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1.3. Time Series Plot in History

Time Series Analysis Ch1. Introduction

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1.4. An Overview of the Book

Time Series Analysis Ch1. Introduction

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Exercises:

1. Simulate a completely random process of length 48 withindependent, normal values. Plot the time series plot. Does it lookrandom?

2. Simulate a completely random process of length 48 withindependent, chi-square distributed values, each with 2 degrees offreedom. Display the time series plot. Does it look random andnonnormal?

Time Series Analysis Ch1. Introduction

Page 12: Ch1. Introduction - people.missouristate.edupeople.missouristate.edu/songfengzheng/Teaching/MTH548/Time Series... · Time Series Analysis Ch1. Introduction. 1.3. Time Series Plot

Time Series Analysis Ch1. Introduction

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Time Series Analysis Ch1. Introduction

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Time Series Analysis Ch1. Introduction

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Time Series Analysis Ch1. Introduction

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Time Series Analysis Ch1. Introduction

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Time Series Analysis Ch1. Introduction