FORECASTING

1
FORECASTING

• A Brief Introduction to Forecasting Using
  Econometric and Time Series Models

2
Two Broad Approaches

• Econometric forecasting
• Based on a causal, regression model
• Conditional vs Unconditional Forecasting
• Use of Leading Indicators
• Times Series forecasting
• Decomposes time series into a time trend, a
  seasonal factor, a cyclical element and an error
  term
• History provides guide to the future

3
Econometric Models

• Four Potential Sources of Error
• Specification error
• Conditioning error
• Sampling error
• Random error
• Forecasting Confidence Intervals

4
Confidence Interval
5
Miscellany

• If model has serially correlated errors that you
  corrected with GLS, do not use GLS model to
  forecast.
• With simultaneous systems (no lagged endogenous
  variables), use reduced form model to forecast.
• If dependent variable in log form, must adjust
  forecast to eliminate bias.

6
Trend Line Fitting
7
Trend Line Fitting

• Assumes that past behavior will continue
• Used to generate short run forecasts
• Used to detrend data so as to explain
  fluctuations around the trend

8
Time Series Models

• Autoregressive model
• Yt is a function of Yt-1, Yt-2, and a white
  noise error term
• Moving average model
• Yt is a linear combination of past values of the
  error series
• ARMA models
• Mixture of autoregressive and moving average
  models

9
ARMA or ARIMA Model
AR(p,q)
10
Stationarity

• Stationary time series is one where dependent
  variable has a constant mean and variance over
  time. Nonstationary series exhibits some sort of
  upward or downward trend over time.
• ARIMA model can only be applied to stationary
  series. To convert nonstationary to stationary,
  take first differences

11
Steps in Time Series Modeling

• Identification -- specification of p,d and q
• Estimation
• Diagnostic checking
• Forecasting

12
Identification

• Examine plots of data , the ACF, the correlogram
  to choose d
• Choose p and q through iterative process designed
  to eliminate autoregressive and moving average
  components. The residuals should be white noise.
  Examine the ACF and the PACF

13
Behavior of ACF and PCF
14
Diagnostic Checking

• Box-Pierce statistic
• Ljung-Box test statistic