**Forecasting** Statistical Terms

## Demand planning, inventory planning and demand forecasting.

### A

### averaging period

The number of historical data points used in moving average computations. *See **also *moving average.

### B

### bootstrapping

A statistical forecasting technique based on sampling at random (with replacement) from historical values. These resampled data values are combined to form realistic demand scenarios that resemble the actual historical demand patterns without exactly repeating them.

### Brown’s method

An exponential smoothing forecasting method appropriate for data with trend but without seasonality. Also known as DOUBLE exponential smoothing

### C

### coefficient of variation

A measure of the relative variability of the data values stored in a variable, computed as 100 times the standard deviation divided by the mean.

### correlation

A measure of the degree of linearrelationship between two variables, ranging from -1 to +1, with 0 indicating no linear relationship.Large values may suggest a leading indicatorrelationship useful in regression analysis.

### crosscorrelation

The correlation between oneseries and another one that is shifted forward or backward in time. *See *correlation.

### cross-sectional data

Data organized by administrative units rather than by time periods(for example, company sales measured over all sales territories during one time period).

### cumulative forecast

The forecast of the total of all the data values over the forecast horizon. Use this number when your goal is to estimate percentiles of the cumulative demand. The cumulative forecast differs from the forecast sum when the service level is not 50%. *See *forecast sum.

### D

### data cycle

The frequency with which data are collected. If the data are collected in monthly “buckets,” the data cycle is 12. Quarterly data have a data cycle of 4. Accounting months have a data cycle of 13. If you have a web site and you want to track usage by the hour, you may want to use a data cycle of 24.

### decomposition

A statistical procedure that decomposes a time series into trend, seasonal, and irregular components. In multiplicative decomposition, data = trend x seasonal x irregular. In additive decomposition, data = trend + seasonal+ irregular. *See also *seasonal adjustment.

### d.f.

Degrees of freedom. Used in computing the statistical significance of an F-statistic in a regression analysis.

### dependent variable

In regression analysis, the variable to be predicted from the predictor or independent variable(s). Also known as the forecast variable. In the equation Y = 1 + 2 X, the dependent variable is Y.

### .DOUBLE exponential smoothing

A forecasting method appropriate for data with trend but without seasonality. Also known as Brown’s method.

### dummy variable

A variable that takes on only the values of zero or one. This type of variable is often used in regression analysis to indicate the presence or absence of some factor, such as a price promotion or a snowstorm. These play a role similar to event variables in promo/event modeling.

### Durbin-Watson statistic

In regression analysis, an indicator of the degree of autocorrelation in theresiduals. Values near 2 indicate no autocorrelation, values between 0 and 2 indicate positive autocorrelation, and values between 2 and 4 indicate negative autocorrelation. If the DW is not near 2, the regression equation may still be useful for forecasting purposes, but it is not the best summary you could make of the historical relationships among your variables; furthermore, the estimates of uncertainty will be inaccurate.

### E

### EOQ models

Economic Order Quantity models. A class of models designed to find efficient inventory control procedures. For instance, one type of EOQ model computes the best values for when to reorder and how much to reorder, so as to balance inventory carrying costs against the cost of losing sales due to stockouts.

### event model

A forecasting model used in Promo forecasting that adjusts the data for the effects of unusual events, then applies exponential smoothing. Events include sales promotions, bad weather, power outages, and other unusual circumstances of short duration.

### exponential smoothing

A class of forecasting methods that averages out the random variation in a data series. Exponential smoothing computes a weighted average of all the historical data in a series. It gets its name from the way it weights the data, giving each data point a fixed percentage of the weight assigned to its successor. SmartForecasts uses the following four exponential smoothing methods: single, double, Winters’ additive and Winters’ multiplicative.

### F

### fit or fitted value

In regression analysis, the statistical approximation to the actual value of the forecast or dependent variable.

### forecast

A prediction about the future value of a variable.

### forecast interval

In SmartForecasts, the range of values indicating the margin of error in the forecast.

### F-statistic

In regression analysis, an indicator of the collective ability of all the predictor (independent) variables to predict the forecast (dependent) variable. The F-statistic is used to assess the chance that a high value of R-square is nothing more than a statistical fluke. It is possible to get a fairly high value of R-square just by accident, especially when you have a small number of data cases relative to the number of predictor variables. With more data, you might get a much lower R-square. The statistical significance of a given value of the F-statistic must be assessed manually using a table of critical values and the degrees of freedom reported by SmartForecasts. If the F-statistic is not statistically significant, then none of the predictors is useful. Examine the tstatistics for individual regression coefficients only if the F-statistic is significant. *See also *d.f.statistical significance, coefficient, and t-statistic.

### H

### hedge

A judgmentally specified deceleration of a statistical trend.

### holdout analysis

A method for making realistic assessments of forecast uncertainty. This method uses older data values to forecast newer values, then compares the forecasted and actual values. This mimics reality, since the forecasts are assessed against data that were not involved in their creation. There are two versions. A simple holdout analysis compares the most recent actual data values against forecasts using all the previous data. A sliding simulation uses a portion of the historical data to forecast the next several values, then slides forward one period and repeats the process, and continues in this way until using all but the last data value to predict one step ahead

### I

### independent variable

*See *predictor variable.

### intermittent demand

Demand that is mostly zero,but takes random nonzero values at random times. Intermittent demand is characteristic of spare parts and high-priced capital goods. Also known as “slow moving demand,” “lumpy demand,” “irregular demand.” and “sporadic demand.”

### interval forecast

A forecast expressed as a range, for example, there is a 90% chance that sales next month will be between 100 and 150 units. *See *point forecast.

### inventory optimization

The process of computing the minimal inventory needed to provide a desired inventory service level.

### irregular component

The random variation in a time series that remains after trend and seasonality have been accounted for. The irregular component measures the effect of other influences on the series, such as snowstorms, strikes, power failures, and other nonrecurring events. *See *decomposition.

### L

### lag

The number of time periods that old values are shifted forward to pair with current values when computing an autocorrelation.

### .lead

The number of time periods that future values are shifted backward to pair with current values when computing an autocorrelation.

### lead time

In inventory management, the time between placing and receiving an inventory replenishment order. The inventory manager may wish to insure that there are no stockouts during this period.

### lead time demand

The total of the demands in each period of the lead time.

### leading indicator

An item or variable whose changes anticipate changes in some other variable.For example, knowing current new car sales may let you better predict next quarter’s sales of automotive aftermarket accessories. A leadingindicator can be used as a predictor variable in regression analysis.

### least squares

A method of estimating regression coefficients. This method selects values for theregression constant and coefficients so as tominimize the sum of squared residuals. *See also *regression and residual.

### level

A feature of a time series indicating its longtermaverage value.

linear moving average A forecasting method appropriate for data with trend but without seasonality; also useful for removing seasonality from trending data. Sometimes referred to as double moving average.

### M

### mean

A measure of the typical level of a variable,computed as the arithmetic average of the data values stored in the variable.

### measure

A numeric value to be forecasted. It might be unit sales, liters, dollars, and so on.

### median

A measure of the typical level of a variable, determined by sorting the values stored in a variable from smallest to largest and identifying the middle value (if there are an odd number of data values) or the average of the two middle values (if there are an even number of data values).

### moving average

A class of forecasting methods for averaging out the random variation in a data series. A moving average uses only the most recent to form the total, forecasts the total, then pro-rates the forecasts of the total down to the individual items.

### N

### noise

A term describing the net effect of any number of random factors that influence the value of a variable. The Decompose feature separates noise from the trend and seasonality in a variable.

### outlier

A data value that is much larger or smaller than the other values of the same variable. An outlier could be caused by an error in data recording or an unusual circumstance.

### P

### P(2-tail)

In regression analysis, the probability that a regression coefficient would achieve its observed value or an even greater value solely by chance, if the true coefficient value were zero. A low value of P(2-tail) suggests that the coefficient is not zero. *See *statistically significant.

### percentile

A number that equals or exceeds a specified percentage of all the values of a variable. For instance, the median is the 50th percentile, since 50% of the data values are less than or equal to the median.

### point forecast

A forecast expressed as a single number, for example, sales next month will most likely be 125 units. *See *interval forecast.

### predictor variable

In regression analysis, a variable used to forecast the dependent or forecastvariable. Also known as an independent variable. In the equation Y = 1 + 2X, the predictor variable is X.

### Promotional forecasting

A special feature of SmartForecasts that combines automatic forecasting with adjustments for sales promotions and other special events that influence sales, such as blizzards and strikes.

### Q

### quartile

A number that divides the distribution of data values into quarters. The lower quartile is greater than 25% of the data values, the middle quartile (that is, the median) is greater than 50%, and the upper quartile is greater than 75%.

### R

### regression

A statistical analysis that creates an equation to convert the values of predictor or independent variables into estimates of the values of a forecast or dependent variable

### residual

In regression analysis, the difference between the actual value of the forecast, or dependent variable, and its fitted value.

### R-square

In regression analysis, a measure of goodness of fit between the observed and fitted values of the forecast or dependent variable. Rsquare values range from 0% to 100%, with 100% indicating a perfect fit. If the R-square is close to 0%, then your predictors are essentially worthless for forecasting purposes. *See *adjusted R-square

### S

### safety stock

An inventory buffer or investment that must be added to the most likely estimate of future demand (that is, the expected forecast) to protect against demand variablity

### scatterplot

A graph of cross-sectional data, with the independent variable on the horizontal (X) axis and the dependent variable on the vertical (Y) axis. Also known as XY plot.

### seasonal adjustment

A statistical procedure to cancel out a predictable pattern of monthly, quarterly, or other periodic variation in a data series. If the seasonality is multiplicative, seasonal adjustment divides the data by seasonal multipliers. If the seasonality is additive, seasonal adjustment subtracts seasonal add-factors from the data. The Decompose command performs seasonal adjustment to leave only the influences of the trend and irregular components. *See *decomposition

### seasonal component

The repetitive cyclical influence on a time series. The Decompose command estimates the trend, seasonal, and irregular components.

### seasonality

A feature of a time series characterized by repetitive cycles of high and low values; often found in quarterly data (cycles of period 4) and monthly data (cycles of period 12).

### Series

A sequence of measurements or observations on a variable.

### service level

The probability, expressed as a percentage, of meeting total customer demand for a particular product item during a future period out of available inventory (for example, inventory nextperiod will be sufficient to maintain a 95% or 99% customer service level). Also known as inventory service level.

### service level forecasts

Forecasts of a high percentile of the distribution of demand. Usually, forecasts aim for the average or expected valueHowever, in inventory control applications, it is important to plan around the upper end of the demand distribution; this helps to minimize the occurrence of stockouts or backorders.

### SIMPLE moving average

A forecasting method appropriate for data with neither trend nor seasonality; also useful for removing seasonality from data without trend.

### simulation

A method of understanding the randomness in a variable by creating scenarios or possible futures. Used to estimate the distribution of lead time demand when forecasting intermittent data.

### SINGLE

exponential smoothing A forecasting method appropriate for data with neither trend nor seasonality.

### SKU

Abbreviation for Stock Keeping Unit, the most disaggregated level of inventory tracked in a manufacturing company.

### smoothed data value

In forecasting method using exponential smoothing or moving averages, the statistical approximation to the actual value of the forecast variable.

### smoothing weight

The percentage weight given to the most recent data value in exponential smoothing computations. A lower weight implies more smoothing.

### sparcity

The percentage of variables containing historical data. If sparcity is eliminated when connecting a database to SmartForecasts, only rows with forecastable historical data are imported into the SmartForecasts’ data table.

### standard deviation

A measure of the variability of the data values stored in a variable (computed using n-1 in the denominator).

### standard error

In regression analysis, a measure of the sampling uncertainty in the value of a regression coefficient. If you were to analyze a different set of data on the same subject, you would inevitably get somewhat different regression coefficients. The standard errors show how different the regression coefficients might be. With different data, you could expect to get regression coefficients that are one or even two or more standard errors different from those computed from your present dataset.

### standard error of estimate

In regression analysis, a measure of the typical size of the discrepancies between the actual data values and the values predicted by the regression equation, that is, the residuals. Also known as the root mean square error.

### statistically significant

A result that is beyond the typical range of chance variability. For example, if you flip 100 fair coins, getting 53 heads and 47 tails is not a statistically significant deviation from the 50:50 ideal, since this small a discrepancy is easily explained by chance. In contrast, a 90:10 split would be statistically significant, since this large a discrepancy would almost never arise by chance if the coins were fair. In regressionanalysis, SmartForecasts tests the statistical significance of the regression coefficients against the null hypothesis that they are zero. *See also *P(2-tail)

### T

### timeplot

A graph of data values plotted against time. It is a good idea to examine a timeplot before forecasting to look for trends, seasonality, and unusual values (outliers). Also known as a line graph in Excel.

### time series

An ordered succession of numbers representing the values of a particular variable over a given period of time (for example, monthly sales figures for l999). Synonymous with data series. Contrast with cross-sectional data.

### time table

A table that contains textual attributes

### transformation

Application of a mathematical function to a variable. For instance, log(X) is a transformation of X. Transformations are used to make a skewed distribution more symmetric or to make a nonlinear relationship more linear. The Scatterplot command can transform either or both of the X and Y variables to create a better straight line fit and then save the transformed variables in the data table. The Define command can also create and save new, transformed variables.

### trend

A feature of a time series marked by more or less steady increases or decreases in the level of the series

### trend component

The slow, long-term change in the level of a time series. The Decompose command estimates the trend, seasonal, and irregular components

### trend percent

The average unit change per period divided by average units per period multiplied by It is available as a statistic in the describe function and for numerical filtering to identify variables with positive, negative, or zero trend and to compare average trends of one series with another.

### t-statistic

In regression analysis, the ratio of a coefficient value to its standard error. SmartForecasts uses the t-statistic to compute the value of P(2-tail) when testing the hypothesis that the coefficient value would be zero except for chance variation. Roughly speaking, values of the t-statistic beyond ± 2 suggest that the corresponding predictor variable is useful for predicting the forecast variable. *See *P(2-tail) and statistically significant

### W

### weight

A parameter in an exponential smoothing method that determines the balance of influence between recent and older data values. Higher values for weights give more influence to more recent data values. This permits faster adjustment to changing conditions at the cost of less smoothing of noise when conditions are stable.

### WINTERS’ exponential smoothing

A forecasting method appropriate for data with both trend and seasonality; both additive and multiplicative forms of Winters’ method are available in SmartForecasts.