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HansensSlides-Forecasting.pdf

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2/12/2019

Forecasting Methods

Professor Jared M. Hansen, Ph.D.

Running Average Forecasting

This forecasting technique works well if trend is fairly constant and if seasonality is not present in the data.

The procedure takes past periods and averages them. The average is the sales forecast.

Each period, the forecast drops the oldest period and adds the most recent period.

The major cause for error in this example is the seasonality of the time series, the running average model doesn't model seasonality.

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Seasonal Factors

• Seasonal factors are most often multiplicative variables in the forecasting model. Sometimes an additive seasonal factor is calculated.

• Each month, forecasts use one of twelve different seasonal factors--one for each month of the year.

• Seasonal factors modify forecasts to match the peaks and valleys that seasonality causes in a time series.

Seasonal Factors

Two problems: • First, since only one year is used, one atypical month

causes erroneous seasonal factors to be calculated. An atypical event, such as a strike or price promotion, affects sales; and the seasonal factor reflects the atypical event rather than the seasonal nature of the time series. To eliminate this problem, forecasters generally use at least two years' data in calculating seasonal factors, or they modify or change the atypical data to reduce the impact of the atypical event.

• The second problem with the procedure is that the date has trend; that is, sales are increasing over time. This trend effect is interpreted as seasonal effect. Removing the trend in the data before seasonal factors are calculated eliminates this problem.

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The Exponential Smoothing Model

• This model has received widespread acceptance among American business firms that employ sales forecasts for managerial planning and control.

• Exponential smoothing models use special weighted moving averages and a seasonal factor that is multiplied by the weighted moving average to calculate the forecast.

• These weighted moving averages are referred to as smoothing statistics. The exponential smoothing models are an extension of the running average model.

The Exponential Smoothing Model

• Generally, exponential smoothing uses three smoothed statistics that are weighted, so that the more recent the data, the more weight given the data in producing a forecast.

• These three averages are referred to as single, double, and triple smoothing statistics and are running averages that are weighted in an exponential declining method.

• Most forecasting systems use three separate forecasting equations: one model called a constant model, a second called a linear model, and a third called a quadratic model. The constant forecast uses only the single smoothed statistic and is best when the time series has little trend. The linear forecast model uses the single and double smoothed statistics and is best when there is a linear trend in the time series. The quadratic forecast model uses all three statistics--single, double, and triple smoothed

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ARIMA Models

• One of the most widely used techniques for short- term forecasting is the autoregressive integrated moving average (ARIMA) model that is often associated with G. E. P. Box and G. M. Jenkins

• The ARIMA forecasting model takes into account what is called the signature of a time series. A signature is a pattern in the time series that allows the series to be classified as belonging to a particular group of time series

ARIMA Models

• One of the most widely used techniques for short-term forecasting is the autoregressive integrated moving average (ARIMA) model that is often associated with G. E. P. Box and G. M. Jenkins

• This forecasting technique is somewhat mathematically tedious and complex. It relies of using past sales data exclusively.

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ARIMA Models

• Although the process is involved and difficult to work with, it has great potential for producing a forecasting model with greater accuracy than other techniques, and computer programs greatly simplify the process.

• Several comparative studies have shown the Box-Jenkins technique can, in some cases, produce a forecast which is significant and more statistically accurate than regression or exponential smoothing forecasting models

• Box and Jenkins postulate that a model which is a mix of (1) autoregressive (AR) and (2) moving average (MA) processes can describe a large number of stationary time series.