Computation Section
Subunit Forecasting
 - Simulate

The Simulate option is for the comparison of different forecasting methods on a single time series using simulated data. The process is similar to the Compare option, but here the simulation is live in that the model parameters can be changed on the worksheet and the series and forecasts are automatically adjusted. The option is useful to illustrate the impact of trends, steps and noise on forecasts and their accuracy.


The dialog allows selection of a name, time horizon, history and number of extra columns. The check boxes at the bottom select one or more forecasting methods. The fields to the right of the check boxes indicate how many forecasts of each type are to placed on the worksheet.

Clicking the data model button presents the Model Data dialog. Here we set the initial parameters of the simulated model. The same button appears on the other options for setting the parameters of the simulated data. In addition to determining the integrality and nonnegativity of the data, the option allows the user to introduce random changes in trend and random steps in the base of the time series. For both steps and trends the probability specified determines the chance that a change will occur at any given period. The mean and standard deviation of the magnitude of the change, if it occurs, is also given here. The Base SD is the standard deviation of the noise added to the model. The parameters are used with Monte Carlo simulation to determine the time series. The model assumes that change and noise values are governed by Normal distributions.

The simulation requires a number of additional columns on the worksheet. The Hide Simulation button allows these columns to be hidden. The particular model simulated here has an initial trend of 1, but no step or trend changes.

On clicking OK a worksheet is created with the same name as the forecast. The simulation parameters are placed in the corner of the worksheet. Changing any parameter changes the simulated series.

The columns showing the simulation are shown below. One or more columns of random numbers appear first. The example is affected by only noise so only column F is necessary. The numbers in cells F11 through F40 are simulated from a uniform distribution with range 0 through 1. The numbers are controlled by a seed appearing in cell F9. The simulation can be regenerated by using the Fill Down option on the Change menu item.


Columns G though J hold the base, trend and cumulative trend. The cumulative trend is added to the base to determine the mean value for the model. The Noise in column K is simulated with the Monte Carlo method using the random numbers in row F. The noise values are drawn from a Normal distribution with mean 0 and standard deviation 5. The standard deviation is stored in cell B6.

The value of the time series is the sum of the model and the noise. For the example we round this sum to the nearest integer.

  In the example, we use both an exponential forecast and an exponential forecast with trend. First consider the exponential smoothing results. With simulation, we know both the series value and the model. Column O holds the one period forecast error comparing the observation in one period with the forecast in the previous period. Note that the standard deviation of the error is approximately the noise standard deviation. The error has a positive bias because exponential smoothing estimates always lag for a series with a positive trend. The model error computes the difference between the model and the estimate from the previous period. The bias in the model error is about the same, but the standard deviation is much lower because the error does not include the noise variation of the observation.
  When we include the trend estimate, the bias for both observation errors and model errors is much smaller. Again we note the smaller standard deviation for the model errors. Although this example shows a negative bias, the bias should tend toward zero as more observations are included. With the chosen values of alpha and beta, the initial estimate of the trend is reflected throughout the 20 period time horizon.
To illustrate a more complicated simulation, we create a second model with both step and trend changes. The model dialog is at the left.

The parameters are on the left and the simulated time series is shown below. We note two step changes in the first three periods and four trend changes in 30 periods of the analysis. It is useful to simulate complicated time series to observe the response of forecast methods to various kinds of changes.

Changing the parameters or the random number seeds, results in a different simulated time series.

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tree roots

Operations Management / Industrial Engineering
by Paul A. Jensen
Copyright 2004 - All rights reserved