Question: Assume we have the following time series data on variable Y below: YEAR/Time Y=Output 1953 482 1954 312 1955 1221 1956 1800 1957 2419 1958

Assume we have the following time series data on variable Y below:

YEAR/Time Y=Output

1953 482

1954 312

1955 1221

1956 1800

1957 2419

1958 2958

1959 3454

1960 3897

1961 4317

1962 4705

1963 5056

1964 5378

1965 5681

1966 5964

1967 6216

1968 6425

1969 6632

1970 6836

1971 7003

1972 7170

1973 7315

1974 7456

1975 7595

1976 7715

1977 7815

1978 7918

1979 7995

1980 8079

1981 8164

1982 8239

1983 8292

1984 8355

1985 8402

1986 8461

1987 8493

1988 8539

1989 8561

1990 8609

1991 8649

1992 8660

1993 8680

1994 8726

1995 8740

1996 8760

1997 8783

1998 8805

1999 8812

2000 8854

2001 8841

2002 8869

2003 8893

2004 8883

2005 8888

2006 8904

2007 8913

2008 8913

2009 8923

2010 8948

2011 8962

a) Fit a simple trend model to the time series data and discuss the findings.

b) Fit a quadratic trend model to the time series and discuss the findings: (square time).

c) Compare your results in part (b) to part (a) and use the best of the two models to forecast 2012 and 2013 values of Y.

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