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QMT 3001 BUSINESS FORECASTING

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Exploring Data Patterns&

A I d i F i T h iAn Introduction to Forecasting Techniques

Aysun KAPUCUGİL-İKİZ, PhD.

Forecasting 2

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Time Series Data Patterns

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The two steps in analyzing time series data are:(a) Graph the time series data

Horizontal (stationary) / Trend / Cyclical / Seasonal

(a) Graph the time series data The data should be graphed to visually see the type of pattern: is

the series progressively increasingor is it decreasing through time?

There are various graphing techniques available including scatter diagrams, line graphs, or bar graphs. You can choose the visual approach that is optimal for your data.

(b) Generate an autocorrelation function(b) Generate an autocorrelation function The pattern of the autocorrelations will usually help explain the

pattern of the data. The autocorrelation output will also provide you with statistical tests to determine if the autocorrelation is important(i.e., "significant" in statistical terms).

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A stationary data series does not increaseor decrease overtime.

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= observation in time period t

= observation at time period t-k

tY

ktY

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Stat > Time Series > Autocorrelation

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randomness

trend

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seasonality

Is AC significant?

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The standard error is the The standard error is the difference between a predicted value and the actual value for avariable. If the autocorrelation coefficient isdivided by the standard error, the outcome should be >2 for a significant outcome.

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"Box-Ljung Statistic" (BLS) or modified Box-Pierce Q Statistic:o ju g S a s c ( S) o od ed o e ce Q S a s c:.05 or less of level of significance value of Box-Ljung, is desirable -this means the forecaster has a less than a 5% chance of being wrong in stating autocorrelation exists between two variables.

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r1= 0.572

r2= 0.463

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Differencing data is needed when forecasting two data patterns:1. Data with a trend.2. Data with a strong autocorrelation component at lag 1 (above 0.90), where the autocorrelation at subsequent lags diminishes slowly.

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Differencing simply generates a new time series by subtracting the current value from the previous value for the entire original series.value from the previous value for the entire original series.

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Examples37 Examples

Example:"Anna-Marie's Pools and Spas" is a chain of stores in Manitoba selling pools and pool supplies.

Anna-Marie is considering opening a new store in Saxon, Manitoba and has

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approached you as an advisor.

She has a number of markets she is considering for her new store and wants to carefully examine each of these markets before making her selection.

She wants to know if this is a good year to open a new store in Saxon, or if she would be better advised to wait a few years.

She has asked you to examine the pattern of pool sales in Saxon in past years, using data on pool permits as a proxy for sales. Table shows this data for the last 15 years.

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The first step is to graph this data over time.

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The next step in the analysis is to generate the autocorrelation function, to see if the data is indeed random.

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Correlogram41

Example:Table shows the number of houses under construction (housing starts) in July in Toronto for the period 1994 to 2004.

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Scatter graph43

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Housing under Construction in Toronto, Monthly, from January 1972 to May 2005(extended the housing data series back to 1972 and include all months, rather than just July.)

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To illustrateTo illustrate a cyclical pattern

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For forecasting purposes this indicates that the future values will dependon the last available level.However, using this approach to forecast cyclical time-series is problematic

When time series data changes by smallmargins from period to period, the bestapproach is to

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ppexplore how the datamoves (e.g., the rate of change).

"differencing".

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An example of differenced data for the firstfive rows of the Housing Under Construction database.

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= 39455 - 41744

Differenced Data48

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When is the best

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Example:

time for the new home builder to hold open houses in order to time these with the

ddi k ?wedding market?

Table shows the number of marriages recorded in Canada from 1995 to 2004, on a quarterly basis (3 month intervals).

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Side-by-side Bar Chart51

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The optimal forecasting technique for anygiven situation depends on the nature ofavailable data and the decision to be madeor problem to be solved.

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Other Factors for Choosing a Forecasting Technique: Level of Details.

Time horizon.

Based on judgment or data manipulation.

Management acceptance.

Cost.

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Types of Forecasts

Forecasting Techniques

No single method is superior

MovingAverage

Exponential Smoothing

Time-Series Methods: include historical data over a time interval

DelphiMethods

Jury of ExecutiveOpinion

Qualitative Models: attempt to include subjective factors

Causal Methods: include a

variety of factors

Regression Analysis

Multiple Regression

Trend ProjectionsSales ForceComposite

ConsumerMarket Survey

Decomposition

General considerations for choosing the appropriate method

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Method Uses ConsiderationsJ d C b d i h b f S bj i i bj hJudgment Can be used in the absence of

historical data (e.g. new product).Most helpful in medium- and long-term forecasts

Subjective estimates are subject to the biases and motives of estimators.

Causal Sophisticated methodVery good for medium- and long-term forecasts

Must have historical data.Relationships can be difficult to specifylong term forecasts specify

Time series Easy to implement Work well when the series is relatively stable

Rely exclusively on past data. Most useful for short-term estimates.

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Example:Check the quality of forecast of the data on July Housing Under Construction

Compare two forecasts using:

d f h h l d

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1. the second naïve forecast (which includes a difference term)

2. moving average method

The in-sample period will be 1994 to 2002, p p ,

the out-of-sample check will use the years 2003 and2004.

First step: Check the errors of the forecast for autocorrelation.

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Results for the naïve forecast74

Results for the moving average forecast75

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Results for the moving average forecast76

Second step: Check the errors for 2003 and 2004 and test which forecast produces a more accurate result.

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the "in-sample" test78

the "out-of-sample" test79

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The out-of-sample test confirms the results of the in-sample test.

The error measures are all much larger for the moving average forecast

than they are for the naïve forecast.

This confirms that the naïve forecast is superior for short-term forecasts

for this data.

REFERENCES

Business Forecasting. John E. Hanke and Dean W. Wichern 9th Edition Pearson Ed cation 2009

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Wichern, 9th Edition, Pearson Education, 2009.