Time Series Analysis (Business Statistics Tutorial )
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The document discusses time series data, which consist of statistical observations collected at successive time intervals. It highlights the role of time series analysis in understanding past behavior, planning for the future, and evaluating current performance, while also outlining four basic types of variations in time series: secular trend, seasonal variations, cyclical variations, and irregular variations. Additionally, it explains that secular trends can be either linear or non-linear and provides examples of fitting trends to production data over time.
Time Series Analysis (Business Statistics Tutorial )
- 2. Time Series • We often use / deal with statistical data which are collected, observed or recorded at successive intervals of time to determine the consistency of gathering information from the past data. Such data are considered as time series. • When we observe data (numerical) at different points of time.The set of observation is known as time series.
- 3. Mathematically • Mathematically , a time series is defined by the values Y₁ ,Y₂ --------- of a variableY at time t₁ , t₂ -------- Thus Y is a function of t . SymbolizedY = F (t). Example : Production, Sales, Profits of a company at different points of time say over the last 5 years.
- 4. Role of Time Series Analysis • 1) It helps in the understanding of the past behavior of observed data. • 2) It helps in planning future operations. • 3) It helps in evaluating current accomplishments. • 4) It helps to facilitate comparison.
- 5. Component of Time Series • There are four basic types of variations which associates the changes in the series over a period of time. 1) SecularTrend. 2) SeasonalVariations. 3) CyclicalVariations. 4) IrregularVariations.
- 6. • Any particular variableY in a series can be expressed as a product of these components Y =T x S x C x I Where,T = Secular trend. S = SeasonalVariations. C= CyclicalVariations. I = IrregularVariations.
- 7. Secular Trend • We often talk that the population, prices, production normally increases day to day.We observe such variables over a long period of time. Some times we find variables showing downward or constant tendency such death rate of babies by diarrhea. All these variable we observe for a long time which is known as a secular trend.
- 8. Types of Secular trends. There are two types of Secular trends. 1) Linear or Straight line trends. 2) Non Linear trends. The straight line trends is represented by the equation. Yc = a+bx Where,Yc denotes the trend values to distinguished from the actual valueY. ∑ Y a is theY intercept & a = N
- 9. Types of Secular trends. • b is the amount of change inY which associate with the change of unit in X variable. ∑XY b = ∑X²
- 10. Example : • Nakib’s factory produces sugar in different years as follows. 1) Fit a straight line trend to these figure. 2) Estimate the likely sales of the company during 2005. Year 201 0 2011 2012 2013 2014 2015 2016 Production (in m.tonnes) 80 90 92 83 94 99 92
- 11. Math Solution