time series analysis
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This document provides an overview of time series analysis and its key components. It discusses that a time series is a set of data measured at successive times joined together by time order. The main components of a time series are trends, seasonal variations, cyclical variations, and irregular variations. Time series analysis is important for business forecasting, understanding past behavior, and facilitating comparison. There are two main mathematical models used - the additive model which assumes data is the sum of its components, and the multiplicative model which assumes data is the product of its components. Decomposition of a time series involves discovering, measuring, and isolating these different components.
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time series analysis
- 1. TIME SERIES ANALYSISITS COMPONENTSMODELSOVERVIEW Prepared By Sachin Awasthi Varun JainNausheen
- 3. A time series is……A set of data depending on the time
- 4. A series of values over a period of time
- 5. Collection of magnitudes belonging to different time periods of some variable or composite of variables such as production of steel, per capita income, gross national income, price of tobacco, index of industrial production.Time is act as a device to set of common stable reference point.In time series, time act as an independent variable to estimate dependent variables
- 6. Mathematical presentation of Time SeriesA time series is a set of observation taken at specified times, usually at ‘equal intervals’. Mathematically a time series is defined by the values Y1, Y2…of a variable Y at times t1, t2…. Thus,Y= F(t)
- 7. CAUSES OF VARIATIONS IN TIME SERIES DATASocial customs, festivals etc.SeasonsThe four phase of business : prosperity, decline, depression, recoveryNatural calamities: earthquake, epidemic, flood, drought etc.Political movements/changes, war etc.
- 8. IMPORTANCE OF TIME SERIES ANALYSIS
- 9. A very popular tool for Business Forecasting.Basis for understanding past behavior.Can forecast future activities/planning for future operationsEvaluate current accomplishments/evaluation of performance.Facilitates comparisonEstimation of trade cycle
- 10. Time Series - ExamplesStock price, SensexExchange rate, interest rate, inflation rate, national GDPRetail salesElectric power consumptionNumber of accident fatalities
- 11. COMPONENTS OF TIME SERIES
- 12. WHAT IS COMPONENTS?Characteristic movements or fluctuations of time series.
- 14. SECULAR TREND OR TRENDThe general tendency of the data to grow or decline over a long period of time.The forces which are constant over a long period (or even if they vary they do so very gradually) produce the trend. For e.g., population change, technological progress, improvement in business organization, better medical facility etc. E.g., Formation of rocks
- 15. Downward trend-declining death rateUpward trend-population growthMathematically trend may be Linear or non-linear
- 17. SEASONAL VARIATIONS/FLUCTUATIONSThe component responsible for the regular rise or fall (fluctuations) in the time series during a period not more than 1 year.Fluctuations occur in regular sequence (periodical)The period being a year, a month, a week, a day, or even a fraction of the day, an hour etc. Term “SEASONAL” is meant to include any kind of variation which is of periodic nature and whose repeating cycles are of relatively short duration.The factors that cause seasonal variations are: (a) Climate & weather condition, (b) Customs traditions & habits
- 18. CHACTERISTICS/FEATURES OF SEASONAL VARIATIONSRegularityFixed proportionIncrease or DecreaseEasy fore cast
- 19. PURPOSE OF MEASURING SEASONAL VARIATIONSAnalysis of past behavior of the seriesForecasting the short time fluctuationsElimination of the seasonal variations for measuring cyclic variations
- 20. EXAMPLES OF SEASONAL VARIATIONSCrops are sown and harvested at certain times every year and the demand for the labourgowing up during sowing and harvesting seasons.Demands for wollen clothes goes up in winterPrice increases during festivalsWithdraws from banks are heavy during first week of the month.The number of letter posted on Saturday is larger.
- 21. CYCLIC VARIATIONSCycle refers to recurrent variations in time seriesCyclical variations usually last longer than a yearCyclic fluctuations/variations are long term movements that represent consistently recurring rises and declines in activity.
- 22. BUSINESS CYCLEConsists of 4 phases: prosperity, decline, depressions, recovery
- 23. purposeMeasures of past cyclical behaviorForecastingUseful in formulating policies in business
- 24. IRREGULAR VARIATIONSAlso called erratic, random, or “accidental” variations Do not repeat in a definite patternStrikes, fire, wars, famines, floods, earthquakesunpredictable
- 25. CHARACTERISTICSIrregular & unpredictableNo definite patternShort period of timeNo Statistical technique
- 26. ANALYSIS OR DECOMPOSITION OF TIME SERIES
- 28. Measuring
- 29. Isolating
- 30. Components of the time seriesMATHEMATICAL MODELS OF TIME SERIESAdditive model1. We assume that the data is the sum of the time series components.Yt = T + S + C + I2.If the data do not contain one of the components (e.g., cycle) the value for that missing component is zero. Suppose there is no cycle, then Yt = T + S + I3.The seasonal component is independent of trend, and thus magnitude of the seasonal swing is constant over time. Multiplicative model 1. We assume that the data is the product of the various components. Yt = T× S ×C × I2.If trend, seasonal variation, or cycle is missing, then the value is assumed to be 1.Suppose there is no cycle, then Yt = T× S × I3. The seasonal factor of multiplicative model is a proportion (ratio) to the trends, and thus the magnitude of the seasonal swing increases or decreases according to the behavior of trend .
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