Question: 1. Generate a simple random walk data. Apply first-order differencing. Did it remove non-stationarity? Apply second-order differencing. Did it remove non-stationarity? 2. Consider the immigration

1. Generate a simple random walk data. Apply first-order differencing. Did it remove non-stationarity? Apply second-order differencing. Did it remove non-stationarity?

2. Consider the immigration data from BB. Stationary? If not stationary then try to stationarize the data.

3. Consider the Monthly Australian Beer Consumption data from BB. Decompose the data and interpret. What are the seasonal effects for January and July? What is the de-seasonalized forecast if the production on September 1995 is 140?

immigration data

yr count
1820 8385
1821 9127
1822 6911
1823 6354
1824 7912
1825 10199
1826 10837
1827 18875
1828 27382
1829 22520
1830 23322
1831 22633
1832 60482
1833 58640
1834 65365
1835 45374
1836 76242
1837 79340
1838 38914
1839 68069
1840 84066
1841 80289
1842 104565
1843 52496
1844 78615
1845 114371
1846 154416
1847 234968
1848 226527
1849 297024
1850 369980
1851 379466
1852 371603
1853 368645
1854 427833
1855 200877
1856 200436
1857 251306
1858 123126
1859 121282
1860 153640
1861 91918
1862 91985
1863 176282
1864 193418
1865 248120
1866 318568
1867 315722
1868 138840
1869 352768
1870 387203
1871 321350
1872 404806
1873 459803
1874 313339
1875 227498
1876 169986
1877 141857
1878 138469
1879 177826
1880 457257
1881 669431
1882 788992
1883 603322
1884 518592
1885 395346
1886 334203
1887 490109
1888 546889
1889 444427
1890 455302
1891 560319
1892 579663
1893 439730
1894 285631
1895 258536
1896 343267
1897 230832
1898 229299
1899 311715
1900 448572
1901 487918
1902 648743
1903 857046
1904 812870
1905 1026499
1906 1100735
1907 1285349
1908 782870
1909 751786
1910 1041570
1911 878587
1912 838172
1913 1197892
1914 1218480
1915 326700
1916 298826
1917 295403
1918 110618
1919 141132
1920 430001
1921 805228
1922 309556
1923 522919
1924 706896
1925 294314
1926 304488
1927 335175
1928 307255
1929 279678
1930 241700
1931 97139
1932 35576
1933 23068
1934 29470
1935 34956
1936 36329
1937 50244
1938 67895
1939 82998
1940 70756
1941 51776
1942 28781
1943 23725
1944 28551
1945 38119
1946 108721
1947 147292
1948 170570
1949 188317
1950 249187
1951 205717
1952 265520
1953 170434
1954 208177
1955 237790
1956 321625
1957 326867
1958 253265
1959 260686
1960 265398
1961 271344
1962 283763
1963 306260
1964 292248
1965 296697
1966 323040
1967 361972
1968 454448
1969 358579
1970 373326
1971 370478
1972 384685
1973 398515
1974 393919
1975 385378
1976 499093
1977 458755
1978 589810
1979 394244
1980 524295
1981 595014
1982 533624
1983 550052
1984 541811
1985 568149
1986 600027
1987 599889
1988 641346
1989 1090172
1990 1535872
1991 1826595
1992 973445
1993 903916
1994 803993
1995 720177
1996 915560
1997 797847
1998 653206
1999 644787
2000 841002
2001 1058902
2002 1059356
2003 703542
2004 957883
2005 1122257
2006 1266129
2007 1052415
2008 1107126
2009 1130818
2010 1042625
2011 1062040
2012 1031631
2013 990553
2014 1016518
2015 1051031
2016 1183505

Australian

Month Monthly beer production in Australia: megalitres. Includes ale and stout. Does not include beverages with alcohol percentage less than 1.15. Jan 1956 ? Aug 1995
1956-01 93.2
1956-02 96
1956-03 95.2
1956-04 77.1
1956-05 70.9
1956-06 64.8
1956-07 70.1
1956-08 77.3
1956-09 79.5
1956-10 100.6
1956-11 100.7
1956-12 107.1
1957-01 95.9
1957-02 82.8
1957-03 83.3
1957-04 80
1957-05 80.4
1957-06 67.5
1957-07 75.7
1957-08 71.1
1957-09 89.3
1957-10 101.1
1957-11 105.2
1957-12 114.1
1958-01 96.3
1958-02 84.4
1958-03 91.2
1958-04 81.9
1958-05 80.5
1958-06 70.4
1958-07 74.8
1958-08 75.9
1958-09 86.3
1958-10 98.7
1958-11 100.9
1958-12 113.8
1959-01 89.8
1959-02 84.4
1959-03 87.2
1959-04 85.6
1959-05 72
1959-06 69.2
1959-07 77.5
1959-08 78.1
1959-09 94.3
1959-10 97.7
1959-11 100.2
1959-12 116.4
1960-01 97.1
1960-02 93
1960-03 96
1960-04 80.5
1960-05 76.1
1960-06 69.9
1960-07 73.6
1960-08 92.6
1960-09 94.2
1960-10 93.5
1960-11 108.5
1960-12 109.4
1961-01 105.1
1961-02 92.5
1961-03 97.1
1961-04 81.4
1961-05 79.1
1961-06 72.1
1961-07 78.7
1961-08 87.1
1961-09 91.4
1961-10 109.9
1961-11 116.3
1961-12 113
1962-01 100
1962-02 84.8
1962-03 94.3
1962-04 87.1
1962-05 90.3
1962-06 72.4
1962-07 84.9
1962-08 92.7
1962-09 92.2
1962-10 114.9
1962-11 112.5
1962-12 118.3
1963-01 106
1963-02 91.2
1963-03 96.6
1963-04 96.3
1963-05 88.2
1963-06 70.2
1963-07 86.5
1963-08 88.2
1963-09 102.8
1963-10 119.1
1963-11 119.2
1963-12 125.1
1964-01 106.1
1964-02 102.1
1964-03 105.2
1964-04 101
1964-05 84.3
1964-06 87.5
1964-07 92.7
1964-08 94.4
1964-09 113
1964-10 113.9
1964-11 122.9
1964-12 132.7
1965-01 106.9
1965-02 96.6
1965-03 127.3
1965-04 98.2
1965-05 100.2
1965-06 89.4
1965-07 95.3
1965-08 104.2
1965-09 106.4
1965-10 116.2
1965-11 135.9
1965-12 134
1966-01 104.6
1966-02 107.1
1966-03 123.5
1966-04 98.8
1966-05 98.6
1966-06 90.6
1966-07 89.1
1966-08 105.2
1966-09 114
1966-10 122.1
1966-11 138
1966-12 142.2
1967-01 116.4
1967-02 112.6
1967-03 123.8
1967-04 103.6
1967-05 113.9
1967-06 98.6
1967-07 95
1967-08 116
1967-09 113.9
1967-10 127.5
1967-11 131.4
1967-12 145.9
1968-01 131.5
1968-02 131
1968-03 130.5
1968-04 118.9
1968-05 114.3
1968-06 85.7
1968-07 104.6
1968-08 105.1
1968-09 117.3
1968-10 142.5
1968-11 140
1968-12 159.8
1969-01 131.2
1969-02 125.4
1969-03 126.5
1969-04 119.4
1969-05 113.5
1969-06 98.7
1969-07 114.5
1969-08 113.8
1969-09 133.1
1969-10 143.4
1969-11 137.3
1969-12 165.2
1970-01 126.9
1970-02 124
1970-03 135.7
1970-04 130
1970-05 109.4
1970-06 117.8
1970-07 120.3
1970-08 121
1970-09 132.3
1970-10 142.9
1970-11 147.4
1970-12 175.9
1971-01 132.6
1971-02 123.7
1971-03 153.3
1971-04 134
1971-05 119.6
1971-06 116.2
1971-07 118.6
1971-08 130.7
1971-09 129.3
1971-10 144.4
1971-11 163.2
1971-12 179.4
1972-01 128.1
1972-02 138.4
1972-03 152.7
1972-04 120
1972-05 140.5
1972-06 116.2
1972-07 121.4
1972-08 127.8
1972-09 143.6
1972-10 157.6
1972-11 166.2
1972-12 182.3
1973-01 153.1
1973-02 147.6
1973-03 157.7
1973-04 137.2
1973-05 151.5
1973-06 98.7
1973-07 145.8
1973-08 151.7
1973-09 129.4
1973-10 174.1
1973-11 197
1973-12 193.9
1974-01 164.1
1974-02 142.8
1974-03 157.9
1974-04 159.2
1974-05 162.2
1974-06 123.1
1974-07 130
1974-08 150.1
1974-09 169.4
1974-10 179.7
1974-11 182.1
1974-12 194.3
1975-01 161.4
1975-02 169.4
1975-03 168.8
1975-04 158.1
1975-05 158.5
1975-06 135.3
1975-07 149.3
1975-08 143.4
1975-09 142.2
1975-10 188.4
1975-11 166.2
1975-12 199.2
1976-01 182.7
1976-02 145.2
1976-03 182.1
1976-04 158.7
1976-05 141.6
1976-06 132.6
1976-07 139.6
1976-08 147
1976-09 166.6
1976-10 157
1976-11 180.4
1976-12 210.2
1977-01 159.8
1977-02 157.8
1977-03 168.2
1977-04 158.4
1977-05 152
1977-06 142.2
1977-07 137.2
1977-08 152.6
1977-09 166.8
1977-10 165.6
1977-11 198.6
1977-12 201.5
1978-01 170.7
1978-02 164.4
1978-03 179.7
1978-04 157
1978-05 168
1978-06 139.3
1978-07 138.6
1978-08 153.4
1978-09 138.9
1978-10 172.1
1978-11 198.4
1978-12 217.8
1979-01 173.7
1979-02 153.8
1979-03 175.6
1979-04 147.1
1979-05 160.3
1979-06 135.2
1979-07 148.8
1979-08 151
1979-09 148.2
1979-10 182.2
1979-11 189.2
1979-12 183.1
1980-01 170
1980-02 158.4
1980-03 176.1
1980-04 156.2
1980-05 153.2
1980-06 117.9
1980-07 149.8
1980-08 156.6
1980-09 166.7
1980-10 156.8
1980-11 158.6
1980-12 210.8
1981-01 203.6
1981-02 175.2
1981-03 168.7
1981-04 155.9
1981-05 147.3
1981-06 137
1981-07 141.1
1981-08 167.4
1981-09 160.2
1981-10 191.9
1981-11 174.4
1981-12 208.2
1982-01 159.4
1982-02 161.1
1982-03 172.1
1982-04 158.4
1982-05 114.6
1982-06 159.6
1982-07 159.7
1982-08 159.4
1982-09 160.7
1982-10 165.5
1982-11 205
1982-12 205.2
1983-01 141.6
1983-02 148.1
1983-03 184.9
1983-04 132.5
1983-05 137.3
1983-06 135.5
1983-07 121.7
1983-08 166.1
1983-09 146.8
1983-10 162.8
1983-11 186.8
1983-12 185.5
1984-01 151.5
1984-02 158.1
1984-03 143
1984-04 151.2
1984-05 147.6
1984-06 130.7
1984-07 137.5
1984-08 146.1
1984-09 133.6
1984-10 167.9
1984-11 181.9
1984-12 202
1985-01 166.5
1985-02 151.3
1985-03 146.2
1985-04 148.3
1985-05 144.7
1985-06 123.6
1985-07 151.6
1985-08 133.9
1985-09 137.4
1985-10 181.6
1985-11 182
1985-12 190
1986-01 161.2
1986-02 155.5
1986-03 141.9
1986-04 164.6
1986-05 136.2
1986-06 126.8
1986-07 152.5
1986-08 126.6
1986-09 150.1
1986-10 186.3
1986-11 147.5
1986-12 200.4
1987-01 177.2
1987-02 127.4
1987-03 177.1
1987-04 154.4
1987-05 135.2
1987-06 126.4
1987-07 147.3
1987-08 140.6
1987-09 152.3
1987-10 151.2
1987-11 172.2
1987-12 215.3
1988-01 154.1
1988-02 159.3
1988-03 160.4
1988-04 151.9
1988-05 148.4
1988-06 139.6
1988-07 148.2
1988-08 153.5
1988-09 145.1
1988-10 183.7
1988-11 210.5
1988-12 203.3
1989-01 153.3
1989-02 144.3
1989-03 169.6
1989-04 143.7
1989-05 160.1
1989-06 135.6
1989-07 141.8
1989-08 159.9
1989-09 145.7
1989-10 183.5
1989-11 198.2
1989-12 186.8
1990-01 172
1990-02 150.6
1990-03 163.3
1990-04 153.7
1990-05 152.9
1990-06 135.5
1990-07 148.5
1990-08 148.4
1990-09 133.6
1990-10 194.1
1990-11 208.6
1990-12 197.3
1991-01 164.4
1991-02 148.1
1991-03 152
1991-04 144.1
1991-05 155
1991-06 124.5
1991-07 153
1991-08 146
1991-09 138
1991-10 190
1991-11 192
1991-12 192
1992-01 147
1992-02 133
1992-03 163
1992-04 150
1992-05 129
1992-06 131
1992-07 145
1992-08 137
1992-09 138
1992-10 168
1992-11 176
1992-12 188
1993-01 139
1993-02 143
1993-03 150
1993-04 154
1993-05 137
1993-06 129
1993-07 128
1993-08 140
1993-09 143
1993-10 151
1993-11 177
1993-12 184
1994-01 151
1994-02 134
1994-03 164
1994-04 126
1994-05 131
1994-06 125
1994-07 127
1994-08 143
1994-09 143
1994-10 160
1994-11 190
1994-12 182
1995-01 138
1995-02 136
1995-03 152
1995-04 127
1995-05 151
1995-06 130
1995-07 119
1995-08 153

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