2 Forecasting Tools and Techniques

FORECASTING TOOLS AND TECHNIQUES: 

FORECASTING TOOLS AND TECHNIQUES Prepared by Norman R. Ramos LGU Finance Advisor, ADB TA 7451-PHI Support to Local Government Financing November 2011

Categorization of Forecasting Methods: 

Categorization of Forecasting Methods Quantitative Qualitative Forecasting Tools and Techniques 2 Sufficient quantitative information is available Time Series -predicting the continuation of historical patterns such as growth in GDP or growth in tax revenues. Explanatory - understanding how explanatory variables such as GDP and the property tax rate affect the real estate market. Little or no quantitative information is available, but sufficient qualitative knowledge exists. Predicting the speed of passage of a set of amendment to the LGC. Forecasting the long-term effects of technology on the consumption of oil.

Categorization of Forecasting Methods: 

Categorization of Forecasting Methods Unpredictable Conditions for the Application of Quantitative Forecasting Forecasting Tools and Techniques 3 Little or no information is available. Predicting the discovery of a new, very cheap form of energy that produces no pollution. Predicting the rate of positive behavioral changes in Philippine politics. Information about the past is available. This information can be quantified in the form of numerical data. Assumption of continuity- some aspects of the past pattern will continue into the future.

Quantitative Forecasting Techniques: 

Quantitative Forecasting Techniques Intuitive or ad hoc methods Formal quantitative methods Forecasting Tools and Techniques 4 Highly judgmental Based on empirical experience that varies widely from activity to activity, product to product and forecaster to forecaster. Simple and easy to use, but not always as accurate as formal quantitative methods. Little or no information about the accuracy of the forecast. Also involve extrapolation, but it is done in a standard way using a systematic approach that attempts to minimize forecasting errors. Although nothing remains exactly the same, some aspects of history do repeat themselves in a sense. Improved is forecasting is possible via the application of the right method to identify the relationship between the variable to be forecasted and time itself or several other variables. Fall on a continuum between two extremes

Quantitative Forecasting Techniques: 

Quantitative Forecasting Techniques Explanatory Forecasting Time Series Forecasting Forecasting Tools and Techniques 5 Variable to be forecasted exhibits an explanatory relationship with one or more explanatory variables. Purpose of explanatory model is to establish the form of the relationship and use it to forecast future values of the forecast variable. Any change in inputs will affect the output of the system in a predictable way assuming the explanatory relationship will not change. Treats the system as a black box and makes no attempt to discover the factors affecting its behavior . Prediction of the future is based on past values of a variable and/or past errors but not on explanatory variables which may affect the system. Objective is to discover the pattern in the historical data series and extrapolate that pattern into the future.

Quantitative Forecasting Techniques: 

Quantitative Forecasting Techniques Choosing the right “model” Optimum Approach Forecasting Tools and Techniques 6 Key is to identify the nature of the relationship. Plot of raw data to decide on the nature of the following: Trend (linear or non-linear) Seasonality Strength of the random component Best forecasts are usually generated by a system combining explanatory and time series models GDP time series model Base GDP Forecasts REGVA Explanatory Model

Statistical Forecasting Methods: 

Forecasting Tools and Techniques 7 Moving Average Analysis : Simple Moving Averages-forecasts future values based on a weighted average of past values-easy to update. Weighted Moving Averages: Very powerful and economical. They are widely used where repeated forecasts required-uses methods like sum-of-the-digits and trend adjustment methods. Adaptive Filtering : A type of moving average which includes a method of learning from past errors-can respond to changes in the relative importance of trend, seasonal, and random factors. Exponential Smoothing : A moving average form of time series forecasting-efficient to use with seasonal patterns- easy to adjust for past errors-easy to prepare follow-on forecasts-ideal for situations where many forecasts must be prepared-several different forms are used depending on presence of trend or cyclical variations. Statistical Forecasting Methods

Statistical Forecasting Methods: 

Forecasting Tools and Techniques 8 Trend Analysis : Uses linear and nonlinear regression with time as the explanatory variable-used where pattern over time. Decomposition Analysis: Used to identify several patterns that appear simultaneously in a time series-time consuming each time it is used-also used to de- seasonalize a series. Nonlinear Regression : Does not assume a linear relationship between variables-frequently used when time is the independent variable. Statistical Forecasting Methods

Statistical Forecasting Methods: 

Forecasting Tools and Techniques 9 Multiple Regression Analysis : Used when two or more independent factors are involved-widely used for intermediate term forecasting. Used to assess which factors to include and which to exclude. Can be used to develop alternate models with different factors. Modelling and Simulation : Model describes situation through series of equations - allows testing of impact of changes in various factors-substantially more time-consuming to construct. Can be very powerful in developing and testing strategies otherwise non-evident. Statistical Forecasting Methods

Statistical Forecasting Methods: 

Forecasting Tools and Techniques 10 Certainty models give only most likely outcome-advanced spreadsheets can be utilized to do "what if" analysis-often done e.g.; with computer-based spreadsheets . Probabilistic Models Use Monte Carlo simulation techniques to deal with uncertainty-gives a range of possible outcomes for each set of events. Forecasting error : All forecasting models have either an implicit or explicit error structure, where error is defined as the difference between the model prediction and the "true" value. Additionally, many data snooping methodologies within the field of statistics need to be applied to data supplied to a forecasting model. Also, diagnostic checking, as defined within the field of statistics, is required for any model which uses data. Statistical Forecasting Methods

Time Series Analysis: 

Time Series Analysis Forecasting Tools and Techniques 11 Time series analysis accounts for the fact that data points taken over time may have an internal structure (such as autocorrelation, trend or seasonal variation) that should be accounted for. Definition of Time Series : An ordered sequence of values of a variable at equally spaced time intervals

Time Series and Forecasting: 

Time Series and Forecasting Forecasting Tools and Techniques 12 Irregular Variation Episodic fluctuations – unpredictable variations in a time series that is due to unusual causes that can be identified like strikes, floods, fire, etc. Residual fluctuations - unpredictable variations in a time series that is due to unusual causes that cannot be identified. Time Series – a collection of data recorded over a period of time – daily, weekly, monthly, quarterly, semestral , annual. Secular Trend – smooth long-term direction of a time series, Cyclical Variation – rise and fall of a time series ver periods longer than 1 year. Seasonal Variation – patterns of change in a time series within a year

Time Series and Forecasting: 

Time Series and Forecasting Secular Trend Cyclical Variation 13 3 year election cycle Upward trend line Forecasting Tools and Techniques

Time Series and Forecasting: 

Time Series and Forecasting Seasonal Variation Episodic Fluctuation 14 Seasonal 4 th Quarter Jump Asian Financial Crisis

Time Series Decomposition: 

Time Series Decomposition Forecasting Tools and Techniques 15 When an underlying pattern exists in a data series, that pattern can be distinguished from randomness by smoothing (averaging) past values. Effect of smoothing is to eliminate randomness so the pattern can be projected into the future and used as forecast. Patterns can be decomposed into sub-patterns that identify each component of the time series. Decomposition assumes that the data are made up as follows: Data = pattern + error = f(trend-cycle, seasonality, error)

Time Series Decomposition: 

Time Series Decomposition Forecasting Tools and Techniques 16 Seasonal factor refers to periodic fluctuations of constant length within a year. Trend-cycle represents longer-term changes in the level of the series sometimes separated into trend and cyclical components. Error is the difference between the combined effects of the two sub-patterns and the actual data, often called the “irregular” or the “remainder” component. Basic Approach Establish the trend-cycle component Isolate the seasonal component Residual is assumed to be randomness

Decomposition Models: 

Decomposition Models Additive Form Multiplicative Form Forecasting Tools and Techniques 17 Y t = S t +T t +E t If magnitude of fluctuations do not vary with the level of the series Y t =S t * T t *E t More prevalent in economic series since most seasonal series have seasonal variation which increases with the level of the series

Time Series Analysis: 

Time Series Analysis Forecasting Tools and Techniques 18 Applications : The usage of time series models is twofold: Obtain an understanding of the underlying forces and structure that produced the observed data Fit a model and proceed to forecasting, monitoring or even feedback and feed forward control. Time Series Analysis is used for many applications such as: Economic Forecasting Sales Forecasting Budgetary Analysis Stock Market Analysis Yield Projections Process and Quality Control Inventory Studies Workload Projections Utility Studies Census Analysis and many, many more...

Time Series Analysis: 

Time Series Analysis Forecasting Tools and Techniques 19 Techniques: The fitting of time series models can be an ambitious undertaking. There are many methods of model fitting, but in this training only the following will be covered: Averaging Methods; Exponential Smoothing Techniques; and Seasonality

Smoothing Techniques: 

Smoothing Techniques Forecasting Tools and Techniques 20 Inherent in the collection of data taken over time is some form of random variation. An often-used technique for reducing of cancelling the effect due to random variation is "smoothing". This technique, when properly applied, reveals more clearly the underlying trend, seasonal and cyclic components. There are 2 distinct groups of smoothing methods Averaging Methods Exponential Smoothing Methods

Averaging Methods: Simple Average: 

Averaging Methods: Simple Average Forecasting Tools and Techniques 21 A manager of a “ lechon manok ” chain wants to know how much sales a typical store makes in ‘000 Peso units. He/she takes a sample of 12 suppliers, at random, obtaining the following results. The computed mean or average of the data = 10. The manager decides to use this as the estimate for the daily sales of a typical store. Is this a good or bad estimate? The Mean squared error ( MSE ) is a way to judge how good a model is. The "error" = true sales minus the estimated amount. The "error squared" is the error above, squared. The "SSE" is the sum of the squared errors. The "MSE" is the mean of the squared errors

Averaging Methods : Simple Average: 

Averaging Methods : Simple Average Forecasting Tools and Techniques 22 So how good was the estimator for the sales of each store? Let us compare the estimate (10) with the following estimates: 7, 9, and 12. That is, we estimate that a typical store will attain sales of 7, or 9 or 12. Performing the same calculations we arrive at: The SSE = 36 and the MSE = 36/12 = 3 . The estimator with the smallest MSE is the best . It can be shown mathematically that the estimator that minimizes the MSE for a set of random data is the mean.

Averaging Methods : Simple Average: 

Averaging Methods : Simple Average Forecasting Tools and Techniques 23 The question arises: C an we use the mean to forecast income if we suspect a trend? A look at the graph on the right shows clearly that we should not do this. The mean is not a good estimator when there are trends .

Averaging Methods : Simple Average: 

Averaging Methods : Simple Average Forecasting Tools and Techniques 24 In summary, The “simple” mean of all past observations is only a useful estimate for forecasting when there are no trends. If there are trends, use different estimates that take the trend into account. The average "weighs" all past observations equally. For example, the average of the values 3, 4, 5 is 4. We know that an average is computed by adding all the values and dividing the sum by the number of values. Another way of computing the average is by adding each value divided by the number of values, or 3/3 + 4/3 + 5/3 = 1 + 1.3333 + 1.6667 = 4. The multiplier 1/3 is called the weight . In general: The s are the weights and of course they sum to 1 .

Averaging Methods : Single Moving Average: 

Averaging Methods : Single Moving Average Forecasting Tools and Techniques 25 An alternative way to summarize the past data is to compute the mean of successive smaller sets of numbers of past data. The general expression for the moving average is: 3 MA for Feb Yr 1 = (266.0+145.9+183.1)/3 5 MA for Mar Yr 1 = (266.0+145.9+183.1+119.3+180.3)/5

Averaging Methods: 

Averaging Methods Forecasting Tools and Techniques 26 The more observations included in the moving average, i.e , the larger the value of k, the smoother the resulting trend-cycle. Black line: actual data Green line: 3 MA Red line: 5 MA

Averaging Methods : Centered Moving Average: 

Averaging Methods : Centered Moving Average Forecasting Tools and Techniques 27 In the previous example, we computed the average of the first 3 and first 5 time periods and placed it next to period 3 and period 5, respectively. When computing a running moving average, placing the average in the middle time period makes sense . This works well with odd time periods, but not so good for even time periods. So where would we place the first moving average when M = 4? Technically, the Moving Average would fall at t = 2.5, 3.5, ... To avoid this problem we smooth the MA's using M = 2. Thus we smooth the smoothed values!

Determining the Appropriate Length of A Moving Average: 

Determining the Appropriate Length of A Moving Average Forecasting Tools and Techniques 28 Larger number of terms increases the likelihood that randomness will be eliminated. However, the longer the length, the more terms are lost in the process of averaging since k data values are required for a k-term average. A k-term moving average requires (k-1)/2 neighboring points on either side of the observation Longer-term moving average tend to smooth out genuine “bumps” or cycles that are of interest.

Seasonal Index Using the Ratio-to-Moving -Average : 

Seasonal Index Using the Ratio-to-Moving -Average Forecasting Tools and Techniques 29 Calculate a 4 quarter moving total. Starting at the 2nd qtr of Yr1 =3.2+2.8+0.8+3.2=10.0 Divide the moving totals by 4 Center the moving averages. Starting at the 3 rd qtr of Year 1 = (2.50+2.450)/2=2.4750 Determine the specific seasonal Observation in Col 3/CMA=0.8/2.4750=32.3 Determine the mean of the specific seasonals Average of each quarter SI Adjust the means to get the typical SI.

De-seasonalizing Data: 

De- seasonalizing Data Forecasting Tools and Techniques 30 Deseasonalized data (DS) Where SI = appropriate seasonal index. By smoothing out the seasonal effects, you get the trend-cycle component, which in most forecasting work is what you are interested in.

Netting Out the Effect of Inflations: 

Netting Out the Effect of Inflations Forecasting Tools and Techniques 31 Implicit Price Index (Current Prices/Constant Prices)*100 Value in Constant Prices [Current Prices/(IPIN/100)]

Exponential Smoothing: 

Exponential Smoothing Forecasting Tools and Techniques 32 Whereas in Single Moving Averages the past observations are weighted equally, Exponential Smoothing assigns exponentially decreasing weights as the observation get older. In other words, recent observations are given relatively more weight in forecasting than the older observations . In the case of moving averages, the weights assigned to the observations are the same and are equal to 1/ N . In exponential smoothing, however, there are one or more smoothing parameters to be determined (or estimated) and these choices determine the weights assigned to the observations.

Single Exponential Smoothing: 

Single Exponential Smoothing Forecasting Tools and Techniques 33 This smoothing scheme begins by setting S 2 to y 1 , where S i stands for smoothed observation or Exponentially Weighted Moving Average (EWMA), and y stands for the original observation. The subscripts refer to the time periods, 1, 2, ..., n . For the third period, S 3 = y 2 + (1- α ) * S 2 ; and so on. There is no S 1 ; the smoothed series starts with the smoothed version of the second observation. This is the basic equation of exponential smoothing and the constant or parameter α is called the smoothing constant .

Single Exponential Smoothing: 

Single Exponential Smoothing Forecasting Tools and Techniques 34 EXCEL Computational Routine Predicts a value that is based on the forecast for the prior period, adjusted for the error in that prior forecast. The tool uses the smoothing constant α , the magnitude of which determines how strongly the forecasts respond to errors in the prior forecast. The speed at which the older responses are dampened (smoothed) is a function of the value of α . When it is close to 1, dampening is quick and when it is close to 0, dampening is slow. Values of 0.2 to 0.3 are reasonable smoothing constants. These values indicate that the current forecast should be adjusted 20 percent to 30 percent for error in the prior forecast. Larger constants yield a faster response but can produce erratic projections. Smaller constants can result in long lags for forecast values.

Single Exponential Smoothing: 

Single Exponential Smoothing Forecasting Tools and Techniques 35 An α =0.3 seems to be the best choice based on the MSE criterion. In practice a damping factor between 0.2 and 0.3 often yield the best results.

Forecasting with Single Exponential Smoothing: 

Forecasting with Single Exponential Smoothing Forecasting Tools and Techniques 36 Forecasting the next point New forecast is previous forecast plus an error adjustment. The forecasting formula is the basic equation 0 < α ≤ 1 t > 0 In other words, the new forecast is the old one plus an adjustment for the error that occurred in the last forecast. The most recent observation y t is weighted by α and the most recent forecast S t by (1- α ). What happens if you wish to forecast from some origin, usually the last data point, and no actual observations are available? In this situation we have to modify the formula to become: where y origin remains constant. This technique is known as bootstrapping

Forecasting with Single Exponential Smoothing: 

Forecasting with Single Exponential Smoothing Using results of previous exponential smoothing estimates For α = 0.1 Yr 13 = (0.1)*70+(1-0.1)*71.665=71.5 Yr 14 = (0.1)*70+(1-0.1)*71.5=71.35 Yr 15 =(0.1)*70+(1.01)*71.35=71.21 Forecasting Tools and Techniques 37 Yr 12 actual value Yr 12 forecast Yr 13 forecast

Double Exponential Smoothing: 

Double Exponential Smoothing Forecasting Tools and Techniques 38 Single Smoothing sometimes does not excel in following the data when there is a trend. This situation can be improved by the introduction of a second equation with a second constant, , which must be chosen in conjunction with α . Here are the two equations associated with Double Exponential Smoothing: 0 ≤ α ≤ 1 0 ≤ γ ≤ 1 Note that the current value of the series is used to calculate its smoothed value replacement in double exponential smoothing.