Definitions [1]
Definition: Time Series
A time series is a sequence of observations made on a variable at regular time intervals over a specified period of time.
Formulae [4]
Formula: Additive Model
\[X_t=T_t+S_t+C_t+I_t\]
Formula: Multiplicative Model
\[X_t=T_t\times S_t\times C_t\times I_t\]
Formula: Method of Moving Averages
First moving average:
\[\frac{X_1+X_2+\cdots+X_k}{k}\]
Second moving average:
\[\frac{X_2+X_3+\cdots+X_{k+1}}{k}\]
Formula: Method of Least Squares
Linear Trend Equation:
\[X_t=a+bt\]
Normal Equations:
\[\sum X_t=na+b\sum t\]
\[\sum tX_t=a\sum t+b\sum t^2\]
Key Points
Key points: Components of Time Series
| No. | Component | Simple Definition |
|---|---|---|
| 1 | Secular Trend (T) | The long-term general direction in which the data moves over time. |
| 2 | Seasonal Variation (S) | Regular changes that repeat within a year. |
| 3 | Cyclical Variation (C) | Long-term up and down movements occur over several years. |
| 4 | Irregular Variation (I) | Sudden and unpredictable changes in data. |
Phases of Business Cycle:
-
Prosperity
-
Recession
-
Depression
-
Recovery
Important Questions [11]
- Moving averages are useful in identifying ______.
- Which of the following can’t be a component of a time series?
- Solve the following problem : Following data shows the number of boxes of cereal sold in years 1977 to 1984.Fit a trend line to the above data by graphical method.
- The following table shows the production of gasoline in U.S.A. for the years 1962 to 1976. Year 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976
- Obtain the trend values for the following data using 5 yearly moving averages: Year 2000 2001 2002 2003 2004 Productionxi 10 15 20 25 30 Year 2005 2006 2007 2008 2009 Productionxi 35 40 45 50 55
- Following table shows the amount of sugar production (in lakh tonnes) for the years 1931 to 1941: Year Production Year Production 1931 1 1937 8 1932 0 1938 6 1933 1 1939 5 1934 2 1940 1 1935
- The complicated but efficient method of measuring trend of time series is ______.
- The following table shows gross capital information (in Crore ₹) for years 1966 to 1975: Years 1966 1967 1968 1969 1970 Gross Capital information 20 25 25 30 35 Years 1971 1972 1973 1974 1975
- Obtain the trend values for the data in using 4-yearly centered moving averages.
- The publisher of a magazine wants to determine the rate of increase in the number of subscribers. The following table shows the subscription information for eight consecutive years:
- The simplest method of measuring trend of time series is ______.
