1. Use the data below and STATA or R to solve the following problems.
   1. Plot the t-bill returns. Calculate the sample mean return on the tbills and report a standard error assuming the returns are IID.Is the IID assumption used to construct the standard errors correct?
   2. Plot the S&P 500 series and look at the autocorrelations. The efficient markets hypothesis says that stock returns should be unpredictable. What do the autocorrelations say about market efficiency?
   3. Find a good model for the S&P500 returns. You can consider AR models, MA models, or ARMA models. Start with simple models and check the residuals to see if they are uncorrelated. Report your results.

Data:

year tbill sp500ret 1926 .03603 .12221 1927 .03092 .317908 1928 .04443 .345442 1929 .04922 -.039449 1930 .02749 -.271714 1931 .00707 -.501676 1932 .00871 .112029 1933 .00465 .575114 1934 .0033 -.000979 1935 .00162 .394364 1936 .00186 .303431 1937 .00444 -.413694 1938 .00044 .344436 1939 .00017 .030982 1940 .00019 -.063702 1941 -.00681 -.108915 1942 .00395 .200034 1943 .00407 .249428 1944 .00398 .195378 1945 .004 .320918 1946 .00382 -.074961 1947 .0057 .052411 1948 .00859 .069826 1949 .01141 .17026 1950 .012 .29351 1951 .01568 .219352 1952 .01907 .180735 1953 .02221 -.013316 1954 .01128 .437801 1955 .01598 .282549 1956 .02778 .072373 1957 .03752 -.106786 1958 .02053 .370623 1959 .03587 .119814 1960 .03843 .013715 1961 .02521 .245721 1962 .02941 -.072775 1963 .03257 .210544 1964 .0377 .155988 1965 .0407 .122686 1966 .05204 -.101589 1967 .04744 .223257 1968 .0555 .110966 1969 .06977 -.078772 1970 .07826 .058419 1971 .04941 .144287 1972 .04212 .178194 1973 .07154 -.149989 1974 .08512 -.277289 1975 .06865 .332963 1976 .05676 .224601 1977 .05414 -.072691 1978 .07361 .075407 1979 .10602 .179987 1980 .12547 .300751 1981 .1646 -.042154 1982 .13199 .217804 1983 .09332 .207265 1984 .11115 .073605 1985 .08527 .287579 1986 .0675 .182324 1987 .0664 .096784 1988 .06861 .162396 1989 .09031 .282833 1990 .08438 -.016794 1991 .06385 .281644 1992 .03917 .0771 1993 .03248 .096344 1994 .04278 .018617 1995 .06092 .325131 1996 .05415 .216017 1997 .05494 .304823 1998 .05303 .281749 1999 .04923 .203023 2000 .06152 -.073411 2001 .04481 -.107767 2002 .01795 -.223559 2003 .0116 .260778 2004 .01308 .107049 2005 .03079 .053583 2006 .04835 .147913