[MUSIC] This week, we are focusing on time series forecasting methods for time series data for when we observe a level component. Last week, we saw an example of a forecasting method, the average, which is one possibility when our data exhibits a level component. It would seem logical that an average of past values of the time series may be a good predictor of future values of the time series. However, in many cases, this is not necessarily so. It will be an appropriate predictor if the time series is reasonably horizontal for its entire span with no systematic changes in level. If the time series has trend, seasonal, or cyclical components, the average of the entire time series will not typically provide a good prediction. Also, it is somewhat illogical that whole observations in the time series, including values in the distant past should have an equal weighting in predicting future values. More recent values are more likely to be better predictors and should be given more weight. The opposite end of the scale is to use a naive forecast, which only uses the most recent values to predict future values. A naive forecast is when the previous periods actual observation becomes this periods forecast, and we ignore the impact of every other observation. With the naive forecasting method, the best predictor of what will happen in the next period is what we are observing in the current period. That's why it's called naive. The two possibilities, the entire average and the naive forecast represent two extremes. The average method takes into account every observed data point, and the naive method only takes the very last observed data point into account. A predictor that may have advantages over both of these methods is using an average of a certain number of the most recent observations. If a fixed number of observations is used for the predictor, as new more recent observations are added, the average should not remain static but move, adding recent values and dropping distant values from the average. This predictor is known as a moving average predictor. A moving average or MA is also predictor for time series that are predominantly horizontal, that is the level of the time series remains similar throughout the entire time series. The degree of the moving average is the number of observations of the time series used in the predictor. For example, a three period MA uses the average of the last three observations in the series. Because it is an average, in this regard, the last three observations have an equal weight in the predictor one-third, while the observations prior to those have zero waiting in the predictor. The degree of the moving average is arbitrary. There are some influencing factors though. The volatility of the time series. The more volatile the series, the larger the random component, the more observation should be included in the MA to smooth the series. The length of the time series. For short time series, a short period MA is advised. The predictive performance. Several alternative MA predictors of varying degrees can be tried. The MA, which has the lowest error criteria such as the mean absolute error or mean squared error, may be the preferred one to go with. Thus, for a moving average forecast of degree q, the average of the previous q periods is the forecast for period t. You essentially sum up the observed data for the previous q periods and then divide by q. A modification of the moving average method is simple exponential smoothing, known as SES. Simple exponential smoothing, SES is another smoothing method for when the time series is predominantly horizontal. The key difference between the SES method and the moving average method is the weights used in the predictor. The moving average method gives every observation in the predictor an equal weighting. Logic would suggest that the most recent observation should have the greatest weight, since it will likely be a better predictor of the future values of the time series. SES adopts a weighted averaging procedure with recent observations given relatively more weight. Later this week, you will see how this forecasting method smooths the volatility in a time series, and hence the name, simple exponential smoothing. The SES forecast is a weighted average of the previous actual data point and the previous forecast. Alpha is a smoothing parameter for the weight, and is thus a value between zero and one. It is called simple exponential smoothing because you can substitute in an equation for F t- 1, which is based on Y t- 2, and F t- 2. And in turn, you can substitute in an equation for F t- 2, which depends on Y t- 3 and F t- 3, and so on. Don't worry, knowing the first equation is all you need. Just like in the moving average, the choice of alpha in simple exponential smoothing is arbitrary. However, there are some influencing factors. The volatility of the time series. The more volatile the series, the lower the value of alpha needed to smooth the time series. A lower value of alpha will have the effect of giving observations in the past a greater weighting than if alpha is higher. The predictive performance. Different values of the smoothing parameter can be tried on a test set of the entire time series, and the predictive performance compared using error criteria such as the MAE or MSE. We will look at a tool in Excel called Silver, which will allow us to try varying values of the parameter alpha and find the alpha that minimizes one of these error criterion, such as minimizing the MSE. Now, just as last week, over to the Excel screen flow videos. I encourage you to download the relevant Excel workbook and work alongside me as you watch the video. Attempt the quizzes to practice what you've learned and receive some feedback on your learning. Check out the weekly discussion board where you can discuss your thoughts, questions, and answers with your peers. [MUSIC]
