#### Description of this paper

##### Year 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1-(Answered)

Description

Question

Three Questions of Stat course-Time series?

Need to use R to finish these three questions

Clearer vision for the questions and data are also attached in the drop box

1. Consider the series annual precipitation in "Lake Michigan" (yearly, 1900-
1986).
(a) Plot the series, obtain its ACF and PACF plots. What is your tentative
conclusion about the type of model that may be suitable for this data?
(b) Fit AR(p) models to this data, p = 0; ::; 5. Select the appropriate one by
using the AICC criterion.
(c) For the selected model in part (b), obtain the parameter estimates and their
standard errors. Plot the residuals. Also obtain the plots of ACF and PACF of
the residuals (15 lags). Do these plots suggest that the model selected in part
(b) a reasonable one? Explain.

2. For each of the following models, generate a mean zero random series of
length n = 500 with 2 = 1 (R function arima.sim), plot the data, and obtain
the ACF and PACF plots (with 25 lags). Comment on the results in each case.
(a) MA(1); = 0:8, (b) MA(2), 1 = 0:4; 2 = ????0:6;
(c) AR(2) with 1 = 0:5; 2 = ????0:6, (d) AR(2) with 1 = ????0:3; 2 = 0:6;
(d) ARMA(1; 2) with = 0:6, 1 = 0:4 and 2 = ????0:6:

3. Let fXtg be a stationary sequence (not necessarily AR(p)) with mean and
autocovariance function . Let us denote (1) by . Show that
(a) the best linear predictor of Xt using Xt????1 is X(f)
t = + (Xt????1 ???? ),
(b) the best linear predictor of Xt????2 using Xt????1 is X(b)
t????2 = + (Xt????1 ???? ),
(c) E(Xt ???? X(f)
t )2 = (1 + 2)(0) ???? 2(1);
(d) E(Xt????2 ???? X(b)
t????2)2 = (1 + 2)(0) ???? 2(1);
(e) Cov(Xt ???? X(f)
t ;Xt????2 ???? X(b)
t????2) = (2) ???? 2(1) + 2(0);
(f) the partial correlation between Xt and Xt????2 given Xt????1 is given by
[(2) ???? 2(1) + 2]=[1 + 2 ???? 2(1)]:

Year

1900

1901

1902

1903

1904

1905

1906

1907

1908

1909

1910

1911

1912

1913

1914

1915

1916

1917

1918

1919

1920

1921

1922

1923

1924

1925

1926

1927

1928

1929

1930

1931

1932

1933

1934

1935

1936

1937

1938

1939

1940

1941

1942

1943

1944

1945

1946

Annual precipitation (inches), Lake Michigan, 1900 to 1986

33.2

27.55

31.81

32.5

31.01

34.83

33.19

31.56

29.29

32.62

26.14

35.26

32.9

29.67

31.57

31.21

34.55

27.15

29.99

30.53

29.02

31.58

32.82

28.86

32.13

25.56

34

32.35

32.83

30.56

22.21

30.95

28.44

29.86

28.04

30

28.39

30.1

36.21

29.47

34.45

33.95

35.62

32.27

29.5

36.61

27.86

1947

1948

1949

1950

1951

1952

1953

1954

1955

1956

1957

1958

1959

1960

1961

1962

1963

1964

1965

1966

1967

1968

1969

1970

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

33.34

29.1

30.57

32.96

37.02

30.11

28.99

36.89

27.55

27.2

30.9

25.99

37.82

34.63

31.43

26.97

24.92

29.56

36.89

29.45

33.33

34.29

31.56

32.86

30.1

34.97

33.98

32.77

35.74

26.54

34.42

33.67

33.18

32.11

31.51

32.86

31.55

29.74

38.98

34.65

Annual precLake Mich 1900 to 1986

Paper#9210315 | Written in 27-Jul-2016

Price : \$22