CHAPTER 22: TIME SERIES ECONOMETRICS: FORECASTING

2 Methods of Forecasting

1.      Autoregressive integrated moving average (ARIMA), popularly known as the Box-Jenkins methodology

To forecast the values of a time series, the basic Box-Jenkins strategy is as follows:

a)      First examine the series for stationarity.

b)      If the time series is not stationary, difference it one or more times to achieve stationarity.

c)      The ACF and PACF of the stationary time series are then computed to find out if the series is purely autoregressive or purely of the moving average type or a mixture of the two.

d)      The tentative model is then estimated.

e)      The residuals from this tentative model are examined to find out if they are white noise.

f)       The model finally selected can be used for forecasting.

2.      Vector autoregression (VAR)

The VAR approach to forecasting considers several time series at a time. The distinguishing features of VAR are as follows:

a)      It is a truly simultaneous system in that all variables are regarded as endogenous.

b)      In VAR modeling, the value of a variable is expressed as the linear function of the past, or lagged, values of that variable and all other variables included in the model.

c)      If each equation contains the same number of lagged variables in the system, it can be estimated by OLS without resorting to any systems methods.

d)      The simplicity of VAR modeling may be its drawback.

e)      If there are several lags in each equation, it is not always easy to interpret each coefficient, especially if the signs of the coefficients alternate.

f)       There is considerable debate and controversy about the superiority of the various forecasting methods.

ü  Approaches to Economic Forecasting

1.      Exponential smoothing methods

2.      Single-equation regression models

3.      Simultaneous-equation regression models

4.      Autoregressive integrated moving average models (ARIMA)

5.      Vector autoregression

ü  Measuring Volatility in Financial Time Series: The ARCH and GARCH Models

Volatility clustering – periods in which they exhibit wide swings for an extended time period followed by a period of comparative tranquility.

·         Autoregressive conditional heterscedasticity (ARCH)

·         Generalized autoregressive conditional heteroscedasticity (GARCH)