Time Series Analysis1


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Time Series Analysis1

  1. 1. Time Series Analysis
  2. 3. Time series Analysis <ul><li>Time series is an arrangement of statistical data in a chronological order i.e ., in accordance with its time of occurrence </li></ul><ul><li>It is a record of observations of a variable over a period of time </li></ul><ul><li>Or </li></ul><ul><li>It is used to detect patterns of change in statistical information over regular intervals of time .On the basis of these information we arrive an estimate of future </li></ul><ul><li>Eg. Yearly Bank rates </li></ul><ul><li>yearly exports </li></ul><ul><ul><li>Yearly national income data </li></ul></ul>
  3. 4. Components of time series <ul><li>1.Long term fluctuations(Trend) or Secular Trend(Tt) </li></ul><ul><li>2.Short term Fluctuations(Periodic changes)(s) </li></ul><ul><ul><ul><li>Seasonal Variation ( St) Cyclical Variation( Ct ) </li></ul></ul></ul><ul><li>Random or irregular Fluctuation(It) </li></ul><ul><ul><ul><li>Eg. Population </li></ul></ul></ul><ul><ul><ul><li>Death </li></ul></ul></ul><ul><ul><ul><li>Currency circulation </li></ul></ul></ul>
  4. 5. Mathematical model for time series <ul><li>This is known as Additive Model- if changes are by constant absolute amounts </li></ul><ul><li>Yt= Tt+St+Ct+It </li></ul><ul><li>This model assumes that all the four components of time series operate independently of each other so that none of these components has any effect on the remaining three </li></ul><ul><li>Yt is the time series value at time t </li></ul>
  5. 6. Multiplicative Model <ul><li>multiplicative model- </li></ul><ul><ul><li>multiplicative model is good </li></ul></ul><ul><ul><li>if the changes are by a constant rate except the trend componentY=T*S*C*R where Y- original data </li></ul></ul><ul><li>This model assumes that the four components of the time series are due to different causes but they are not necessarily independent and they can affect each other </li></ul>
  6. 7. Note <ul><li>Most of the time series relating to economic and business phenomina confirm to the multiplicative model </li></ul>
  7. 8. Mixed Models <ul><li>Y=TCS+I </li></ul><ul><li>Y=T+S+IC </li></ul><ul><li>Y=TC+SI </li></ul><ul><li>Y=T+SCI </li></ul><ul><li>SCI=Y/T </li></ul>
  8. 9. Note <ul><li>If the various forces were in a state of equilibrium then the time series will remain constant </li></ul><ul><li>The sales (y) of a product is influenced by </li></ul><ul><li>Advertisement expenditure </li></ul><ul><li>The price of the product </li></ul><ul><li>Income of people </li></ul><ul><li>Other competitive products in the market </li></ul><ul><li>Tastes,fashions,habits and customs of people </li></ul>
  9. 10. Importance of time series ANALYSIS <ul><li>Identify the various forces which cause variations </li></ul><ul><li>We can isolate, study analyze and measure them independently </li></ul><ul><li>Helps </li></ul><ul><ul><ul><li>to understand the past behaviour of data </li></ul></ul></ul><ul><ul><ul><li>General tendency of the data </li></ul></ul></ul><ul><ul><ul><li>Forecast future behaviour of data </li></ul></ul></ul><ul><ul><ul><li>It helps in evaluating current programmes(compare actual and expected) </li></ul></ul></ul><ul><ul><ul><li>Facilitates comparison </li></ul></ul></ul><ul><li>or influences </li></ul>
  10. 11. Secular Trend or Long term Movement(Tt) <ul><li>The value of the variable tends to increase or decrease or remain the same with passage of time is known as trend. </li></ul><ul><li>Eg. The steady increase of cost of living index by recorded by the consumer Price Index </li></ul><ul><li> </li></ul>
  11. 12. Short time Fluctuations <ul><li>Short time Fluctuation consist of seasonal variation, Cyclic variations and irregular variations </li></ul><ul><li>If trend values are eliminated from the original values then short time fluctuations can be obtained </li></ul><ul><li>If both are same no short term fluctuation </li></ul>
  12. 13. Seasonal Variation <ul><li>The variation which occur with some degree of regularity ,within a specific period of one year or shorter is known as seasonal variation </li></ul>
  13. 14. Cyclic Variation <ul><li>When the period of variation is greater an year and the variation occur not with a degree of regularity is known as cyclic variation </li></ul>
  14. 15. Irregular Variation <ul><li>Variation as a result of unexpected, unusual or accidental events are termed as irregular variation </li></ul>