Lecture Notes

Week2 Yt = a + bt Yt-1 = a + b(t � 1) = a + bt � b yt � yt-1 = a + bt � (a + bt � b) = b et = yt � yt {forecast} MPE measures bias. To eliminate bias, if you have two model, one with positive bias and one with negative bias, the average of those the forecasts from those two models will produce a third model with forecasts with very little bias. Mini tab refers to mse as msd Week4 - natural log smooths out variability relative to the changes in data so if at yr 1 sales is 100 and yr 10 sales is 10000, there is a huge difference and you will have enormous variability yt = B0 + B1*xt +ut ut is the error term Goal is to minimize error data = fit + error yt = yt^ + ut^ yt^ is the fitted values, ut^ is the residual iid - independent and identically distributed - if residuals are not normally distributed (which they are usually are not), they should at least be identically distributed. The Box-Jenkins (ARIMA) Methodology - This approach provides a flowchart of deciding whether or not a model fits a dataset and therefore can be used to forecast - the approach consists of 2 tests: one for the fit of the data, and the other for serial correlation. Based on the significance (t-stats and f-stats), if the model does fit and is significant and if there is no serial correlation, then we can go forward with the model - note: ARIMA does not ensure you are using the best model, only one that meets the criteria that the model fits fairly well and there is no serial correlation ARIMA (p, i (sometimes d), q) - assumptions: assumes there is no trend AR (p) - Autoregressive MA (q) - Moving Average I (i) - Integration (# of times you difference the data to remove the trend) autocorrelations - tell us something about the significance of the moving average coefficients partial autocorrelations - tell us something about the significance of the

autoregressive coefficients Why you wouldn't include a constant: Note this doesn't always apply but the justification is that if the std dev is larger than the mean, this indicates the mean is not statistically significant and the differenced mean would even less significant, as a result, the textbook excludes it ARIMA is good for medium term forecasts as they can predict turning points in the data. The model is not as great for short or long term forecasts.