QM (Time-Series Analysis)

Why are linear models not ideal for use in economic situations?

Expect serial correlation from the residual values

• ideally residual terms are unpredictable and uncorrelated

What do you do if the value being modelled grows exponentially instead of linearly?

Take natural log (and therefore exponent)

ln(y) = b + bt + e, so

y = e^(b + bt + e)

When would a linear model be appropriate, as opposed to a log-linear model?

When the growth is approximately constant

When would a log-linear model be appropriate, as opposed to a linear model?

When the growth is approximately linear

What are the three requirements for a time series to be covariance stationary?

• Constant and finite:

  • expected values in all periods

  • variance in all periods

  • covariance with lagged versions of the time series for all

What happens to time series without covariance stationarity?

• Results are economically invalid

• regression will lead to spurious results

• Estimate of b will be biased

• Hypothesis tests will be invalid

What is an autoregressive model?

Independent variables are historical values of the dependent variables

within AR, what does it mean for a model to be incomplete?

information within the data that the model is not capturing?

How do you correct for an AR model with significant serial correlation (autocorrection) - (Incomplete model)

• Increase number of lags until no significant autocorrect

• Testing for autocorrection in an AR model

• Test for autocorrelation with a t-test

Dubran-Watson Test doesn’t work for AR models (usually works for serial correlation)

When is a time series mean-reverting?

• It falls when level above mean

• It rises when level below mean

How does the formula change for regression for mean-reverting level?

xt = b0 + btxt

Would become:

xt = b0/ (1 - bt)