Mae Powell Hunt[1]

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Mae Powell-HuntMae Powell-HuntProfessor Joseph Professor Joseph

Quantitative MethodsQuantitative Methods

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Assignment #2: Internet Field Assignment #2: Internet Field Trip Trip

““Forecasting”Forecasting”

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Forecasting Definition Forecasting Definition

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1.1. To estimate or calculate in advance, especially to predict To estimate or calculate in advance, especially to predict (weather conditions) by analysis of meteorological data. (weather conditions) by analysis of meteorological data.

2.2. To serve as an advance indication of; foreshadow: price To serve as an advance indication of; foreshadow: price increases that forecast inflation. increases that forecast inflation. (Answers Corporation, 2011)(Answers Corporation, 2011)

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Forecasting Methods two TypesForecasting Methods two Types

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Qualitative Methods has three Qualitative Methods has three DELPHI TECHNIQUE, SCENARIO WRITING, and SUBJECTIVE APPROACH.DELPHI TECHNIQUE, SCENARIO WRITING, and SUBJECTIVE APPROACH.

Quantitative Methods has twoQuantitative Methods has twoTIME SERIES METHODS OF FORECASTING and CAUSAL METHOD OF TIME SERIES METHODS OF FORECASTING and CAUSAL METHOD OF

FORECASTING. FORECASTING.

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QUANTITATIVE FORECASTING QUANTITATIVE FORECASTING METHODSMETHODS

TIME SERIES FORECASTING METHODSTIME SERIES FORECASTING METHODS

In the following topics, we will review techniques that are In the following topics, we will review techniques that are useful for analyzing time series data, that is, sequences of useful for analyzing time series data, that is, sequences of measurements that follow non-random orders. Unlike the measurements that follow non-random orders. Unlike the analyses of random samples of observations that are discussed inanalyses of random samples of observations that are discussed in the context of most other statistics, the analysis of time series the context of most other statistics, the analysis of time series is based on the assumption that successive values in the data file is based on the assumption that successive values in the data file represent consecutive measurements taken at equally spaced represent consecutive measurements taken at equally spaced time intervals. time intervals.

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Two Main GoalsTwo Main Goals There are two main goals of time series analysis: (a) identifying the There are two main goals of time series analysis: (a) identifying the

nature of the phenomenon represented by the sequence of observations, nature of the phenomenon represented by the sequence of observations, and (b) forecasting (predicting future values of the time series variable). and (b) forecasting (predicting future values of the time series variable). Both of these goals require that the pattern of observed time series data is Both of these goals require that the pattern of observed time series data is identified and more or less formally described. Once the pattern is identified and more or less formally described. Once the pattern is established, we can interpret and integrate it with other data (i.e., use it in established, we can interpret and integrate it with other data (i.e., use it in our theory of the investigated phenomenon, e.g., seasonal commodity our theory of the investigated phenomenon, e.g., seasonal commodity prices). Regardless of the depth of our understanding and the validity of prices). Regardless of the depth of our understanding and the validity of our interpretation (theory) of the phenomenon, we can extrapolate the our interpretation (theory) of the phenomenon, we can extrapolate the identified pattern to predict future events. identified pattern to predict future events. ((Interactive Data Corp ,2011)Interactive Data Corp ,2011)

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QUANTITATIVE FORECASTING METHODSQUANTITATIVE FORECASTING METHODSTIME SERIES FORECASTING METHODSTIME SERIES FORECASTING METHODS

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time series forecasting methods are based on analysis of historical data (time series: a set of observations measured at successive times or over successive periods). They make the assumption that past patterns in data can be used to forecast future data points.

1. moving averages (simple moving average, weighted moving average): forecast is based on arithmetic average of a given number of past data points

2. exponential smoothing (single exponential smoothing, double exponential smoothing): a type of weighted moving average that allows inclusion of trends, etc.

3. mathematical models (trend lines, log-linear models, Fourier series, etc.): linear or non-linear models fitted to time-series data, usually by regression methods

4. Box-Jenkins methods: autocorrelation methods used to identify underlying time series and to fit the "best" model (FORECASTING, Unknown)

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QUANTITATIVE FORECASTING METHODSQUANTITATIVE FORECASTING METHODSTIME SERIES FORECASTING METHODSTIME SERIES FORECASTING METHODS

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COMPONENTS OF TIME SERIES DEMANDCOMPONENTS OF TIME SERIES DEMAND 1. average: 1. average: the mean of the observations over time the mean of the observations over time 2. trend:2. trend: a gradual increase or decrease in the average over time a gradual increase or decrease in the average over time 3. seasonal influence:3. seasonal influence: predictable short-term cycling behaviour due to predictable short-term cycling behaviour due to

time of day, week, month, season, year, etc. time of day, week, month, season, year, etc. 4. cyclical movement:4. cyclical movement: unpredictable long-term cycling behaviour due to unpredictable long-term cycling behaviour due to

business cycle or product/service life cycle business cycle or product/service life cycle 5. random error: 5. random error: remaining variation that cannot be explained by the remaining variation that cannot be explained by the

other four components (other four components (FORECASTING, UnknownFORECASTING, Unknown))

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There are several different types of There are several different types of moving averagesmoving averages, which we are going to , which we are going to

explore here, all of which are used by traders to try and smooth out the price explore here, all of which are used by traders to try and smooth out the price

action of a financial instrument, and get a better feel for the longer term action of a financial instrument, and get a better feel for the longer term

direction without all the noise that is often associated with just looking at the direction without all the noise that is often associated with just looking at the

price. In addition to getting a better feel for the longer term trend of a price. In addition to getting a better feel for the longer term trend of a

financial instrument, moving averages are also used to spot potential support financial instrument, moving averages are also used to spot potential support

and resistance levels, and are often used in conjunction with one another to and resistance levels, and are often used in conjunction with one another to

generate buy and sell signals. generate buy and sell signals.

The two most popular types of moving averages are the The two most popular types of moving averages are the Simple MovingSimple Moving

Average (SMA)Average (SMA) and the and the Exponential Moving Average (EMA)Exponential Moving Average (EMA). These. These

moving averages can be used to identify the direction of the trend or define moving averages can be used to identify the direction of the trend or define

potential support and resistance levels. (potential support and resistance levels. (Interactive Data Corp ,1999-2011)Interactive Data Corp ,1999-2011)

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A simple moving average is formed by computing the average price A simple moving average is formed by computing the average price

of a security over a specific number of periods. Most moving of a security over a specific number of periods. Most moving

averages are based on closing prices. A 5-day simple moving averageaverages are based on closing prices. A 5-day simple moving average

is the five day sum of closing prices divided by five. As its name is the five day sum of closing prices divided by five. As its name

implies, a moving average is an average that moves. Old data is implies, a moving average is an average that moves. Old data is

dropped as new data comes available. This causes the average to dropped as new data comes available. This causes the average to

move along the time scale. Below is an example of a 5-day movingmove along the time scale. Below is an example of a 5-day moving

average evolving over three days. average evolving over three days. ((Interactive Data Corp , 1999-2011)Interactive Data Corp , 1999-2011)

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Exponential Moving Average & CalculationExponential Moving Average & Calculation

Daily Closing Prices: 11,12,13,14,15,16,17 First day of 5-day Daily Closing Prices: 11,12,13,14,15,16,17 First day of 5-day

SMA: (11 + 12 + 13 + 14 + 15) / 5 = 13 Second day of 5-day SMA: (11 + 12 + 13 + 14 + 15) / 5 = 13 Second day of 5-day

SMA: (12 + 13 + 14 + 15 + 16) / 5 = 14 Third day of 5-day SMA: (12 + 13 + 14 + 15 + 16) / 5 = 14 Third day of 5-day

SMA: (13 + 14 + 15 + 16 + 17) / 5 = 15 SMA: (13 + 14 + 15 + 16 + 17) / 5 = 15

((Interactive Data Corp ,1999-2011)Interactive Data Corp ,1999-2011)

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Exponential Moving Average & CalculationExponential Moving Average & CalculationThe first day of the moving average simply covers the last five days. The first day of the moving average simply covers the last five days. The second day of the moving average drops the first data point (11)The second day of the moving average drops the first data point (11) and adds the new data point (16). The third day of the moving and adds the new data point (16). The third day of the moving average continues by dropping the first data point (12) and adding average continues by dropping the first data point (12) and adding the new data point (17). In the example above, prices gradually the new data point (17). In the example above, prices gradually increase from 11 to 17 over a total of seven days. Notice that the increase from 11 to 17 over a total of seven days. Notice that the moving average also rises from 13 to 15 over a three day calculation moving average also rises from 13 to 15 over a three day calculation period. Also notice that each moving average value is just below the period. Also notice that each moving average value is just below the last price. For example, the moving average for day one equals 13 last price. For example, the moving average for day one equals 13 and the last price is 15. Prices the prior four days were lower and thisand the last price is 15. Prices the prior four days were lower and this causes the moving average to lag causes the moving average to lag ((Interactive Data Corp ,1999-2011)Interactive Data Corp ,1999-2011)

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Exponential moving averages reduce the lag by applying more weight to Exponential moving averages reduce the lag by applying more weight to recent prices. The weighting applied to the most recent price depends on the recent prices. The weighting applied to the most recent price depends on the number of periods in the moving average. There are three steps to number of periods in the moving average. There are three steps to calculating an exponential moving average. First, calculate the simple calculating an exponential moving average. First, calculate the simple moving average. An exponential moving average (EMA) has to start moving average. An exponential moving average (EMA) has to start somewhere so a simple moving average is used as the previous period's somewhere so a simple moving average is used as the previous period's EMA in the first calculation. Second, calculate the weighting multiplier. EMA in the first calculation. Second, calculate the weighting multiplier. Third, calculate the exponential moving average. The formula below is for aThird, calculate the exponential moving average. The formula below is for a

10-day EMA.10-day EMA. ((Interactive Data Corp ,1999-2011)Interactive Data Corp ,1999-2011)

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SMA: 10 period sum / 10 Multiplier: (2 / (Time periods + 1) ) = (2 / (10 + 1) SMA: 10 period sum / 10 Multiplier: (2 / (Time periods + 1) ) = (2 / (10 + 1) ) = 0.1818 (18.18%) EMA: {Close - EMA(previous day)} x multiplier + ) = 0.1818 (18.18%) EMA: {Close - EMA(previous day)} x multiplier +

EMA(previous day).EMA(previous day). ((Interactive Data Corp ,1999-2011Interactive Data Corp ,1999-2011))

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A 10-period exponential moving average applies an 18.18% weighting to A 10-period exponential moving average applies an 18.18% weighting to the the

most recent price. A 10-period EMA can also be called an 18.18% EMA. A most recent price. A 10-period EMA can also be called an 18.18% EMA. A

20-period EMA applies a 9.52% weighing to the most recent price (2/(20+1) 20-period EMA applies a 9.52% weighing to the most recent price (2/(20+1)

= .0952). Notice that the weighting for the shorter time period is more than = .0952). Notice that the weighting for the shorter time period is more than

the weighting for the longer time period. In fact, the weighting drops by half the weighting for the longer time period. In fact, the weighting drops by half

every time the moving average period doubles.every time the moving average period doubles. ((Interactive Data Corp ,1999-2011)Interactive Data Corp ,1999-2011)

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Below is a spreadsheet example of a 10-day simple moving average and Below is a spreadsheet example of a 10-day simple moving average and a 10-day exponential moving average for Intel. Simple moving averages a 10-day exponential moving average for Intel. Simple moving averages are straight forward and require little explanation. The 10-day average are straight forward and require little explanation. The 10-day average simply moves as new prices become available and old prices drop off. simply moves as new prices become available and old prices drop off. The exponential moving average starts with the simple moving average The exponential moving average starts with the simple moving average value (22.22) in the first calculation. After the first calculation, the value (22.22) in the first calculation. After the first calculation, the normal formula takes over. normal formula takes over. ((Interactive Data Corp ,1999-2011)Interactive Data Corp ,1999-2011)

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Because an EMA begins with a simple moving average, its true value Because an EMA begins with a simple moving average, its true value will not be realized until 20 or so periods later. In other words, the will not be realized until 20 or so periods later. In other words, the value on the excel spreadsheet may differ from the chart value becausevalue on the excel spreadsheet may differ from the chart value becauseof the short look-back period. This spreadsheet only goes back 30of the short look-back period. This spreadsheet only goes back 30periods, which means the affect of the simple moving average has hadperiods, which means the affect of the simple moving average has had20 periods to dissipate. Stockcharts.com goes back 250-periods for its20 periods to dissipate. Stockcharts.com goes back 250-periods for itscalculations so the effects of the simple moving average in the firstcalculations so the effects of the simple moving average in the firstcalculation have fully dissipated calculation have fully dissipated ((Interactive Data Corp ,1999-2011)Interactive Data Corp ,1999-2011)

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QUALITATIVE FORECASTING QUALITATIVE FORECASTING METHODSMETHODS

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qualitative forecasting methods are based on educated opinions of qualitative forecasting methods are based on educated opinions of appropriate persons appropriate persons

1. 1. delphi method:delphi method: forecast is developed by a panel of experts who forecast is developed by a panel of experts who anonymously answer a series of questions; responses are fed back to anonymously answer a series of questions; responses are fed back to panel members who then may change their original responses panel members who then may change their original responses

- very time consuming and expensive - very time consuming and expensive - new groupware makes this process much more feasible - new groupware makes this process much more feasible 2. 2. market research:market research: panels, questionnaires, test markets, surveys, etc. panels, questionnaires, test markets, surveys, etc. 3. 3. product life-cycle analogy:product life-cycle analogy: forecasts based on life-cycles of similar forecasts based on life-cycles of similar

products, services, or processes products, services, or processes 4. 4. expert judgementexpert judgement by management, sales force, or other by management, sales force, or other

knowledgeable persons (knowledgeable persons (FORECASTING, UnknownFORECASTING, Unknown))

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QUALITATIVE FORECASTING QUALITATIVE FORECASTING METHODSMETHODSTrend AnalysisTrend Analysis

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There are no proven "automatic" techniques to identify trend components in the time series data; however, as long as the trend is monotonous (consistently increasing or decreasing) that part of data analysis is typically not very difficult. If the time series data contain considerable error, then the first step in the process of trend identification is smoothing. (StatSoft ElectronicStatSoft Electronic Statistics Textbook, UnknownStatistics Textbook, Unknown)

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QUALITATIVE FORECASTING QUALITATIVE FORECASTING METHODSMETHODS

Trend Analysis SmoothingTrend Analysis Smoothing

Smoothing always involves some form of local averaging of data such thatSmoothing always involves some form of local averaging of data such that the nonsystematic components of individual observations cancel each otherthe nonsystematic components of individual observations cancel each otherout. The most common technique is out. The most common technique is moving averagemoving average smoothing which smoothing which replaces each element of the series by either the simple or weighted average replaces each element of the series by either the simple or weighted average of of nn surrounding elements, where surrounding elements, where nn is the width of the smoothing "window" is the width of the smoothing "window" (see Box & Jenkins, 1976; Velleman & Hoaglin, 1981). Medians can be (see Box & Jenkins, 1976; Velleman & Hoaglin, 1981). Medians can be used instead of means. The main advantage of median as compared to used instead of means. The main advantage of median as compared to moving average smoothing is that its results are less biased by outliers moving average smoothing is that its results are less biased by outliers (within the smoothing window). Thus, if there are outliers in the data (e.g., (within the smoothing window). Thus, if there are outliers in the data (e.g., due to measurement errors), median smoothing typically produces smootherdue to measurement errors), median smoothing typically produces smootheror at least more "reliable" curves than moving average based on the same or at least more "reliable" curves than moving average based on the same window width. The main disadvantage of median smoothing is that in the window width. The main disadvantage of median smoothing is that in the absence of clear outliers it may produce more "jagged" curves than moving absence of clear outliers it may produce more "jagged" curves than moving average and it does not allow for weightingaverage and it does not allow for weighting. . .(StatSoft Electronic Statistics Textbook, .(StatSoft Electronic Statistics Textbook, Unknown)Unknown)

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QUALITATIVE FORECASTING METHODSQUALITATIVE FORECASTING METHODSTrend Analysis Trend Analysis SmoothingSmoothing

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In the relatively less common cases (in time series data), when the measurement error is very large, the distance weighted least squares smoothing or negative exponentially weighted smoothing techniques can beused. All those methods will filter out the noise and convert the data into asmooth curve that is relatively unbiased by outliers (see the respective Sections on each of those methods for more details). Series with relativelyfew and systematically distributed points can be smoothed with bicubicsplines. .(StatSoft Electronic Statistics Textbook, UnknownStatSoft Electronic Statistics Textbook, Unknown)

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QUALITATIVE FORECASTING METHODSQUALITATIVE FORECASTING METHODSTrend Analysis Trend Analysis SmoothingSmoothing

Fitting a function. Fitting a function. Many monotonous time series data can be adequatelyMany monotonous time series data can be adequatelyapproximated by a linear function; if there is a clear monotonous nonlinearapproximated by a linear function; if there is a clear monotonous nonlinearcomponent, the data first need to be transformed to remove the nonlinearity.component, the data first need to be transformed to remove the nonlinearity.Usually a logarithmic, exponential, or (less often) polynomial function canUsually a logarithmic, exponential, or (less often) polynomial function canbe used. be used. .(StatSoft Electronic Statistics Textbook, Unknown).(StatSoft Electronic Statistics Textbook, Unknown)

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QUALITATIVE FORECASTING METHODSQUALITATIVE FORECASTING METHODSTrend Analysis Trend Analysis of Seasonalityof Seasonality

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Seasonal dependency (seasonality) is another general component of the time series pattern. The concept was illustrated in the example of the airline passengers data above. It is formally defined as correlational dependency of order k between each i'th element of the series and the (i-k)'th element (Kendall, 1976) and measured by autocorrelation (i.e., a correlation between the two terms); k is usually called the lag. If the measurement error is not

toolarge, seasonality can be visually identified in the series as a pattern that repeats every k elements. .(StatSoft Electronic Statistics Textbook, UnknownStatSoft Electronic Statistics Textbook, Unknown)

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Autocorrelation correlogram. Autocorrelation correlogram. Seasonal patterns of time series can beSeasonal patterns of time series can beexamined via correlograms. The correlogram (autocorrelogram) displaysexamined via correlograms. The correlogram (autocorrelogram) displaysgraphically and numerically the autocorrelation function (graphically and numerically the autocorrelation function (ACFACF), that is,), that is,serial correlation coefficients (and their standard errors) for consecutive lagsserial correlation coefficients (and their standard errors) for consecutive lagsin a specified range of lags (e.g., 1 through 30). Ranges of two standardin a specified range of lags (e.g., 1 through 30). Ranges of two standarderrors for each lag are usually marked in correlograms but typically the sizeerrors for each lag are usually marked in correlograms but typically the sizeof auto correlation is of more interest than its reliability (see of auto correlation is of more interest than its reliability (see ElementaryConcepts) because we are usually interested only in very strong (and thus) because we are usually interested only in very strong (and thushighly significant) autocorrelations. highly significant) autocorrelations. .(StatSoft Electronic Statistics Textbook, Unknown).(StatSoft Electronic Statistics Textbook, Unknown)

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Examining correlograms. Examining correlograms. While examining correlograms, you should keepWhile examining correlograms, you should keep in mind that autocorrelations for consecutive lags are formally dependent. in mind that autocorrelations for consecutive lags are formally dependent. Consider the following example. If the first element is closely related to the Consider the following example. If the first element is closely related to the second, and the second to the third, then the first element must also be second, and the second to the third, then the first element must also be somewhat related to the third one, etc. This implies that the pattern of serial somewhat related to the third one, etc. This implies that the pattern of serial dependencies can change considerably after removing the first order auto dependencies can change considerably after removing the first order auto correlation (i.e., after differencing the series with a lag of 1). correlation (i.e., after differencing the series with a lag of 1). (StatSoft Electronic(StatSoft Electronic Statistics Textbook, Unknown)Statistics Textbook, Unknown)

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Partial autocorrelations. Partial autocorrelations. Another useful method to examine serial dependencies is to Another useful method to examine serial dependencies is to examine the partial autocorrelation function (examine the partial autocorrelation function (PACFPACF) - an extension of ) - an extension of autocorrelation, where the dependence on the intermediate elements (those autocorrelation, where the dependence on the intermediate elements (those withinwithin

thethelag) is removed. In other words the partial autocorrelation is similar to lag) is removed. In other words the partial autocorrelation is similar to autocorrelation, except that when calculating it, the (auto) correlations with all the autocorrelation, except that when calculating it, the (auto) correlations with all the elements within the lag are partialled out (Box & Jenkins, 1976; see also McDowall, elements within the lag are partialled out (Box & Jenkins, 1976; see also McDowall, McCleary, Meidinger, & Hay, 1980). If a lag of 1 is specified (i.e., there are no McCleary, Meidinger, & Hay, 1980). If a lag of 1 is specified (i.e., there are no intermediate elements within the lag), then the partial autocorrelation is equivalent tointermediate elements within the lag), then the partial autocorrelation is equivalent toauto correlation. In a sense, the partial autocorrelation provides a "cleaner" picture ofauto correlation. In a sense, the partial autocorrelation provides a "cleaner" picture ofserial dependencies for individual lags (not confounded by other serial serial dependencies for individual lags (not confounded by other serial dependencies). dependencies). (StatSoft Electronic Statistics Textbook, Unknown)(StatSoft Electronic Statistics Textbook, Unknown)

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Removing serial dependency. Removing serial dependency. Serial dependency for a particular lag of Serial dependency for a particular lag of kk can be removed by differencing the series, that is converting each can be removed by differencing the series, that is converting each ii'th 'th element of the series into its difference from the (element of the series into its difference from the (i-ki-k)''th element. There are )''th element. There are two major reasons for such transformations. two major reasons for such transformations. (StatSoft Electronic Statistics Textbook,(StatSoft Electronic Statistics Textbook, Unknown)Unknown)

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First, we can identify the hidden nature of seasonal dependencies in the series. Remember that, as mentioned in the previous paragraph,autocorrelations for consecutive lags are interdependent. Therefore,removing some of the autocorrelations will change other auto correlations, that is, it may eliminate them or it may make some other seasonalities moreapparent. (StatSoft Electronic Statistics Textbook, UnknownStatSoft Electronic Statistics Textbook, Unknown)

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ReferenceReference

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Interactive Data Corp ,(1999-2011), StockCharts.com Chat School,.Interactive Data Corp ,(1999-2011), StockCharts.com Chat School,. Moving Averages Moving Averages

http://stockcharts.com/school/doku.php?id=chart_school:technical_indicators:moving_averages#simple_moving_averag

StatSoft Electronic Statistics Textbook, StatSoft Electronic Statistics Textbook, Time Series Analysis, retrieved on 5-7-11, from Time Series Analysis, retrieved on 5-7-11, from http://www.statsoft.com/textbook/time-series-analysis/

David Waring,David Waring,(2007),(2007), Informed trades,Informed trades, Introduction to Simple and exponential moving Introduction to Simple and exponential moving average (EMA) forecasting model and calculation average (EMA) forecasting model and calculation retrieved on 5-7-11, from retrieved on 5-7-11, from http://www.informedtrades.com/3754-introduction-simple-exponential-moving-average-ema-forecasting-model-calculation.html

FORECASTING, FORECASTING, Learning Objectives, Retrieved on 5-7-11, from Learning Objectives, Retrieved on 5-7-11, from http://www.uoguelph.ca/~dsparlin/forecast.htm

Answers Corporation, (2011), The American Heritage Dictionary of the English Language, 4Answers Corporation, (2011), The American Heritage Dictionary of the English Language, 4 thth

edition,edition, forecast forecast, , retrieved on 5-7-11, fromretrieved on 5-7-11, from http://www.answers.com/topic/forecasthttp://www.answers.com/topic/forecast

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The EndThe End

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Mae Powell Hunt[1]