Question

A) 380 370 360 350 01/1985 01/1987 01/1989 01/1991 01/1993 01/1995 01/1997 01/1999 01/2001 01/2003 date B) 15 10 10 15 01/1985 01/1989 01/1993 01/1997 01/2001 01/2005 date C) 2- 2- 01/1985 01/1989 01/1991 01/1993 01/1995 01/1997 01/1999 01/2001 01/2003 date D) 01/1985 01/1987 01/1989 01/1991 01/1993 01/1995 01/1997 01/1999 01/2001 01/2003 01/2005

Answer 1

If the data are collected with respect to time, then such a data-set is referred to as a time series data. There can be variations in a time series due to multiple factors. There are four components of a time-series. They are: Trend, seasonality, cyclical components and random components. The first three components are due to assignable causes and the fourth component is due to chance causes The regular increase or decrease in a time series is called trend. There can be an increasing or a decreasing pattern. If the time series repeats a pattern after definite intervals of time, then such variations are termed as seasonal component. Period of variation for such components is usually less than a year. The repetitive variations in a series which are of the same pattern correspond to cyclical components. The duration of the cyclical component is large, which includes many years. Apart from the known variations in a tome series there exists some variations due to some unknown factors. They are beyond human control and are random in nature. Such variations are called irregular components. The plot in diagram B) clearly displays an upward pattern. There are no repetitions in the series. Therefore, Series B is based on just Trend. The plot in diagram D) shows ups and downs in the graph after regular time intervals. The graphs come back to its initial point within a year. Therefore, Series D is based on just Seasonality. The graph in diagram C) displays both a trend and is repetitive in nature. This graph is composed of trend and seasonality both. Series C is based on Trend and Seasonality both. The carbon dioxide level for December of 2004 is given as 381.6. From the provided data the fitted equation is: 349.4207 +0.1325t The time period for December of 2004 is computed using the above equation as: 381.6 = 349.4207 +0.1325t 32.1793 = 0.1325t 32.1793 0.1325 = 242.86243 t=

Thus, the required time period is 243.