CHAPTER 7 FORECASTING WITH AUTOREGRESSIVE AR MODELS Figure

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CHAPTER 7 FORECASTING WITH AUTOREGRESSIVE (AR) MODELS Figure 7. 1 A Variety of Time

CHAPTER 7 FORECASTING WITH AUTOREGRESSIVE (AR) MODELS Figure 7. 1 A Variety of Time Series Cycles 1 González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc.

7. 1 Cycles Figure 7. 2 Deterministic Cycle González-Rivera: Forecasting for Economics and Business,

7. 1 Cycles Figure 7. 2 Deterministic Cycle González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 2

Figure 7. 3 Unemployed Persons, 1989 -2002 (Seasonally Adjusted) A B D C González-Rivera:

Figure 7. 3 Unemployed Persons, 1989 -2002 (Seasonally Adjusted) A B D C González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 3

7. 2. 1 The AR(1) Process Figure 7. 4 Autoregressive Processes AR(1) González-Rivera: Forecasting

7. 2. 1 The AR(1) Process Figure 7. 4 Autoregressive Processes AR(1) González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 4

Figure 7. 5 Autocorrelation Functions of Covariance-Stationary AR(1) Processes González-Rivera: Forecasting for Economics and

Figure 7. 5 Autocorrelation Functions of Covariance-Stationary AR(1) Processes González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 5

Figure 7. 6 Time Series Plot and Autocorrelation Functions of AR(1) with Negative Parameter

Figure 7. 6 Time Series Plot and Autocorrelation Functions of AR(1) with Negative Parameter González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 6

Figure 7. 7 Per Capita Income Growth (California, 1969 -2002) González-Rivera: Forecasting for Economics

Figure 7. 7 Per Capita Income Growth (California, 1969 -2002) González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 7

7. 2. 2 AR(2) Process Figure 7. 8 Autoregressive Processes AR(2) González-Rivera: Forecasting for

7. 2. 2 AR(2) Process Figure 7. 8 Autoregressive Processes AR(2) González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 8

Figure 7. 9 Nonstationary AR(2) González-Rivera: Forecasting for Economics and Business, Copyright © 2013

Figure 7. 9 Nonstationary AR(2) González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 9

Figure 7. 10 Autocorrelation Functions of Covariance-Stationary AR(2) Processes González-Rivera: Forecasting for Economics and

Figure 7. 10 Autocorrelation Functions of Covariance-Stationary AR(2) Processes González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 10

Figure 7. 11 U. S. Inflation Rate González-Rivera: Forecasting for Economics and Business, Copyright

Figure 7. 11 U. S. Inflation Rate González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 11

Table 7. 1 Estimation Results, U. S. Inflation Rate, AR(2) Model González-Rivera: Forecasting for

Table 7. 1 Estimation Results, U. S. Inflation Rate, AR(2) Model González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 12

Table 7. 2 Multistep Forecast of U. S. Inflation Rate González-Rivera: Forecasting for Economics

Table 7. 2 Multistep Forecast of U. S. Inflation Rate González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 13

Figure 7. 12 U. S. Inflation Rate, Multistep Forecast González-Rivera: Forecasting for Economics and

Figure 7. 12 U. S. Inflation Rate, Multistep Forecast González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 14

7. 2. 3 AR(p) Process Figure 7. 13 Number of Unemployed People Looking for

7. 2. 3 AR(p) Process Figure 7. 13 Number of Unemployed People Looking for Part-Time Work González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 15

7. 3. 1 Deterministic and Stochastic Seasonal Cycles Figure 7. 14 Deterministic Seasonality González-Rivera:

7. 3. 1 Deterministic and Stochastic Seasonal Cycles Figure 7. 14 Deterministic Seasonality González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 16

Figure 7. 15 Stochastic Seasonality González-Rivera: Forecasting for Economics and Business, Copyright © 2013

Figure 7. 15 Stochastic Seasonality González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 17

7. 3. 2 Seasonal ARMA Models Figure 7. 16 Seasonal AR(1) and AR(2), Time

7. 3. 2 Seasonal ARMA Models Figure 7. 16 Seasonal AR(1) and AR(2), Time Series Plots and Autocorrelograms González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 18

Figure 7. 17 Monthly Clothing Sales in the United States. Time Series Plot and

Figure 7. 17 Monthly Clothing Sales in the United States. Time Series Plot and Autocorrelation Functions González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 19

Figure 7. 18 Seasonal MA(1) and MA(2), Time Series Plots and Autocorrelograms González-Rivera: Forecasting

Figure 7. 18 Seasonal MA(1) and MA(2), Time Series Plots and Autocorrelograms González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 20

7. 3. 3 Combining ARMA and Seasonal ARMA Models Figure 7. 19 Monthly Changes

7. 3. 3 Combining ARMA and Seasonal ARMA Models Figure 7. 19 Monthly Changes of Private Residential Construction in U. S. (Millions of Dollars), Time Series Plot and Autocorrelograms González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 21

Table 7. 3 Monthly Changes in Residential Construction. Estimation Results of AR(1) and S-AR(1)

Table 7. 3 Monthly Changes in Residential Construction. Estimation Results of AR(1) and S-AR(1) Model González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 22

Figure 7. 20 Monthly Changes in Residential Construction, Multistep Forecast González-Rivera: Forecasting for Economics

Figure 7. 20 Monthly Changes in Residential Construction, Multistep Forecast González-Rivera: Forecasting for Economics and Business, Copyright © 2013 Pearson Education, Inc. 23

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