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SESSION 53 - 56

SESSION 53 - 56. Last Update 18 th June 2011. Time Series Forecasting. Learning Objectives. Forecasting Time Series Analysis Time Series Forecasting – Linear Trend without Seasonality Time Series Forecasting – Linear Trend with Seasonality. Forecasting - Methodologies.

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SESSION 53 - 56

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  1. SESSION 53 - 56 Last Update 18th June 2011 Time Series Forecasting

  2. Learning Objectives • Forecasting • Time Series Analysis • Time Series Forecasting – Linear Trend without Seasonality • Time Series Forecasting – Linear Trend with Seasonality

  3. Forecasting - Methodologies • Qualitative Methods: Here forecasting is based on intuition, estimates and opinions, typically from the sales force, customers or senior management. Such methods are frequently termed subjective or judgmental. • Causal or Econometric Methods: Forecasting methods that establish causal relationships, such as in regression analysis. For example a motorcar manufacturer would base its demand forecasts on predictions of causal factors such as a) the interest rate, b) price of fuel, c) competitor pricing, d) business confidence indices, e) national income level, etc. • Time Series Methods: These methods are based on the idea that prior occurrences can be used to predict the future, through a process of extrapolation.

  4. Time Series Analysis - Definitions Time series analysis/decomposition breaks-down (decomposes) a time series into its constituent components in order to understand the structure of its pattern. There are four components to a time series: • Secular trend (T) – underlying tendency for the time series to rise (or fall) over time. • Seasonal variation (S) – regular rhythmic pattern e.g. month-end & Christmas sales. • Cyclical variation (C) – a multi-year oscillation due to macro economic or industry level activity. • Irregular variation (I) – unpredictable variations such as a plant breakdown, a strike, etc. These four components may possess an additive or multiplicative relationship:

  5. Example Linear Trend – No Seasonality The table to the left displays the sales of Gold Tomato Sauce glass bottles in ‘000s. Is it possible to predict the future values of the time series for the year 2011 taking into consideration the past trend? The method employed is ignoring seasonal, cyclical or irregular variation.

  6. Plotting Time Series

  7. Guide to Time Series Forecasting excluding Seasonality • Set x values for each time period according to the zero-sum of x rules • Compute all x2 and xy values and sum them • Find the equation of the line: a + b (x) • Use the result of step 3 to compute trend values for each time period • Set future values of x • Calculate y using the future value of x and equation a + b (x)

  8. Step 1 + 2: Set x-Values and compute x2 and xy If n is even: If n is odd:

  9. Step 3 + 4: Determine (T)rend (a+bx)

  10. Step 5 + 6: Set future values of x and estimate y-hat

  11. Chart Forecast

  12. Example Linear Trend - Quarterly Seasonality The table to the left displays an example for the quarterly values of a time series for three consecutive years. It is easy to see that the observed values fluctuate depending on the current quarter. Is it possible to predict the future values of the time series for the year 2000 taking into consideration the quarterly fluctuation? The method employed is ignoring cyclical or irregular variation.

  13. Plotting Time Series

  14. Guide to Time Series Forecasting including Seasonality • Set x values for each time period according to the zero-sum of x rules • Compute all x2 and xy values and sum them • Find the equation of the line: a + b (x) • Use the result of step 3 to compute trend values for each time period • Compute the deviation of actual values from trend values (y / T) • Find the average deviation per time period (e.g. quarter). Adjust values to ∑= 4. • Set future values of x • Determine the future trend values • Input the seasonality values calculated in step 6 • Finalise the sales forecast by multiplying the quarterly trend values by the quarterly seasonality values

  15. Step 1 + 2: Set x-Values and compute x2 and xy If n is even: If n is odd:

  16. Step 3 to 5: Determine (T)rend (a+bx) and compute deviation

  17. Step 6: Find average deviation and adjust to ∑4 Averages across quarters: Rescale to the base of 4:

  18. Step 7 to 10: Set future values of x and estimate y-hat Trend for 2000: Estimate for y:

  19. Chart Forecast

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