Forecasting Basics Two important types of forecasting methods

Forecasting Basics • Two important types of forecasting methods – Extrapolation – Causal • Time Series Notation – Assume we have collected values of a variable over time – Let yt the observation of the variable in period t

Forecasting Basics • Then y 1, y 2, …, yt, … is referred to as a time series. • We will be interested in developing forecasts f 1, f 2, …, ft, … of these values. • People measure the quality of the forecast by measuring how close ft is to yt.

Forecasting Basics • For example, if we wish to use the absolute distance between the forecast and the actual data, we can compute

Moving average forecasts Basic description of method • Each forecast is an average of the several most recent observations • The number of observations in each average is called the span • The larger the span, the less the forecasts react to random noise

Moving average forecasts When applicable • Moving averages work best when: – There is no clear upward or downward trend – There is no seasonality

Developing the spreadsheet model • Step 1: Enter the historical data and create a time series graph – To create the graph, select the series, then choose the “Line” graph option – Since the graph is fairly flat (with only random ups and downs), moving averages is a reasonable forecasting method

Developing the spreadsheet model • Step 2: Calculate the forecasts as averages of 3 previous observations – We’re using a span of 3 here - other spans could be used • Step 3: Calculate absolute forecast errors – Each forecast error is actual minus forecast • Step 4: Calculate MAD, the average of the absolute forecast errors

Developing the spreadsheet model • Step 5: Create a “line” graph that shows the forecasts superimposed on the original time series – Clearly shows how the moving average method “smoothes” the data

Moving average forecasts Sensitivity analysis • Try redoing the analysis with different spans to see the effect of the span on MAD and the final graph

Extrapolation Models • Typically use some weighted combination of past observations to create forecast • What are the weights in the moving average case with a span of 3? • The weights do not have to be equal • We can also use a weighted combination of the last forecast with the last observation