DATA COLLECTION AND ANALYSIS

PRELIMINARY ADJUSTMENTS TO TIME SERIES DATA:

Original form of data base may be in current dollar values. Three adjustments may be necessary:

1. Trading day adjustments

2. Adjustments for price changes

3. Adjustments for changes in population

Trading-Day Adjustments

Raw data is adjusted for the number of trading or working days in the month. Two methods may be used to obtain adjusted data for future analysis.

1. Divide the recorded monthly aggregate by the number of working days per month to get an average daily figure.

2. Determine monthly average trading days over a period of several years. Divide the actual trading days for each year by the monthly average over several years to obtain a trading day coefficient for that month. Divide the actual data by the trading day coefficient to derive the adjusted data.

Adjustment for Changes in Prices

Price changes can cloud the unit change in sales. To adjust for price changes:

1. Select to appropriate price index (but divide by 100)

2. Divide the current value by the appropriate price index to determine the constant dollar value. Note that the constant value is in base year prices.

Adjustments for Changes in Population

The effect of population growth on sales can be adjusted by

1. Dividing by total population to obtain sales per capita

2. Dividing by total households to obtain sales per household.

3. Further demographic influences can be obtained by dividing by population in various age categories, etc.

DATA TRANSFORMATIONS

Linear functions have a constant average change each year. Data with a constant rate of growth each year is nonlinear.

1. Monotonic functions are nonlinear without a point of inflection. Log transformations and quadratic functions are monotonic.

2. Gompertz growth curves have a point of inflection. A polynomial of degree 3 or more can have a point of inflection.

Log Transformation (linear on a ratio scale for y)

log y = a + b t

PATTERNS IN TIME SERIES DATA

Time series data exhibits variation over time in response to four basic influences: Trend, Cyclical, Seasonal, and Irregular. The functional form of the relationship can be as follows:

1. Multiplicative: Y = T x C x S x I

2. Additive: Y = T + C + S + I

In reality, these forces may interact but the decomposition method attempts to segregate and analyze these factors in a systematic fashion.

Sources of Variation in Classical Decomposition Model:

Each of these components is assumed to reflect different influences as follows:

1. Trend forces consist of long-run growth influences, such as changes in technology and demographic changes.

2. Cyclical forces consist of non periodic changes due to business cycle influences.

3. Seasonal forces consist of periodic changes that occur within each year and repeat each year in the same fashion.

4. Irregular forces are either major nonreoccurring events or “white noise” that result in regular and erratic movements over a short period of time.

Estimating the Trend.

1. A least squares regression equation that is based upon data over several business cycles is used to estimate a trend line.

2. The mathematical specification of the line determines if it is linear or nonlinear. (Logarithm or quadratic equation if monotonic or polynomial function if a point of inflection.)

Illustrate with Retail Sales in Memphis example using EXCEL spreadsheet.