6. Process or Product Monitoring and Control
6.4. Introduction to Time Series Analysis
6.4.4. Univariate Time Series Models
6.4.4.1. Sample Data Sets

## Data Set of Southern Oscillations

Source and Background The southern oscillation is defined as the barametric pressure difference between Tahiti and the Darwin Islands at sea level. The southern oscillation is a predictor of el nino which in turn is thought to be a driver of world-wide weather. Specifically, repeated southern oscillation values less than -1 typically defines an el nino. Note: the decimal values in the second column of the data given below are obtained as (month number - 0.5)/12.
Data
``` Southern
Oscillation  Year + fraction  Year       Month
----------------------------------------------

-0.7         1955.04        1955         1
1.3         1955.13        1955         2
0.1         1955.21        1955         3
-0.9         1955.29        1955         4
0.8         1955.38        1955         5
1.6         1955.46        1955         6
1.7         1955.54        1955         7
1.4         1955.63        1955         8
1.4         1955.71        1955         9
1.5         1955.79        1955        10
1.4         1955.88        1955        11
0.9         1955.96        1955        12

1.2         1956.04        1956         1
1.1         1956.13        1956         2
0.9         1956.21        1956         3
1.1         1956.29        1956         4
1.4         1956.38        1956         5
1.2         1956.46        1956         6
1.1         1956.54        1956         7
1.0         1956.63        1956         8
0.0         1956.71        1956         9
1.9         1956.79        1956        10
0.1         1956.88        1956        11
0.9         1956.96        1956        12

0.4         1957.04        1957         1
-0.4         1957.13        1957         2
-0.4         1957.21        1957         3
0.0         1957.29        1957         4
-1.1         1957.38        1957         5
-0.4         1957.46        1957         6
0.1         1957.54        1957         7
-1.1         1957.63        1957         8
-1.0         1957.71        1957         9
-0.1         1957.79        1957        10
-1.2         1957.88        1957        11
-0.5         1957.96        1957        12

-1.9         1958.04        1958         1
-0.7         1958.13        1958         2
-0.3         1958.21        1958         3
0.1         1958.29        1958         4
-1.3         1958.38        1958         5
-0.3         1958.46        1958         6
0.3         1958.54        1958         7
0.7         1958.63        1958         8
-0.4         1958.71        1958         9
-0.4         1958.79        1958        10
-0.6         1958.88        1958        11
-0.8         1958.96        1958        12

-0.9         1959.04        1959         1
-1.5         1959.13        1959         2
0.8         1959.21        1959         3
0.2         1959.29        1959         4
0.2         1959.38        1959         5
-0.9         1959.46        1959         6
-0.5         1959.54        1959         7
-0.6         1959.63        1959         8
0.0         1959.71        1959         9
0.3         1959.79        1959        10
0.9         1959.88        1959        11
0.8         1959.96        1959        12

0.0         1960.04        1960         1
-0.2         1960.13        1960         2
0.5         1960.21        1960         3
0.9         1960.29        1960         4
0.2         1960.38        1960         5
-0.5         1960.46        1960         6
0.4         1960.54        1960         7
0.5         1960.63        1960         8
0.7         1960.71        1960         9
-0.1         1960.79        1960        10
0.6         1960.88        1960        11
0.7         1960.96        1960        12

-0.4         1961.04        1961         1
0.5         1961.13        1961         2
-2.6         1961.21        1961         3
1.1         1961.29        1961         4
0.2         1961.38        1961         5
-0.4         1961.46        1961         6
0.1         1961.54        1961         7
-0.3         1961.63        1961         8
0.0         1961.71        1961         9
-0.8         1961.79        1961        10
0.7         1961.88        1961        11
1.4         1961.96        1961        12

1.7         1962.04        1962         1
-0.5         1962.13        1962         2
-0.4         1962.21        1962         3
0.0         1962.29        1962         4
1.2         1962.38        1962         5
0.5         1962.46        1962         6
-0.1         1962.54        1962         7
0.3         1962.63        1962         8
0.5         1962.71        1962         9
0.9         1962.79        1962        10
0.2         1962.88        1962        11
0.0         1962.96        1962        12

0.8         1963.04        1963         1
0.3         1963.13        1963         2
0.6         1963.21        1963         3
0.9         1963.29        1963         4
0.0         1963.38        1963         5
-1.5         1963.46        1963         6
-0.3         1963.54        1963         7
-0.4         1963.63        1963         8
-0.7         1963.71        1963         9
-1.6         1963.79        1963        10
-1.0         1963.88        1963        11
-1.4         1963.96        1963        12

-0.5         1964.04        1964         1
-0.2         1964.13        1964         2
0.6         1964.21        1964         3
1.7         1964.29        1964         4
-0.2         1964.38        1964         5
0.7         1964.46        1964         6
0.5         1964.54        1964         7
1.4         1964.63        1964         8
1.3         1964.71        1964         9
1.3         1964.79        1964        10
0.0         1964.88        1964        11
-0.5         1964.96        1964        12

-0.5         1965.04        1965         1
0.0         1965.13        1965         2
0.2         1965.21        1965         3
-1.1         1965.29        1965         4
0.0         1965.38        1965         5
-1.5         1965.46        1965         6
-2.3         1965.54        1965         7
-1.3         1965.63        1965         8
-1.4         1965.71        1965         9
-1.2         1965.79        1965        10
-1.8         1965.88        1965        11
0.0         1965.96        1965        12

-1.4         1966.04        1966         1
-0.5         1966.13        1966         2
-1.6         1966.21        1966         3
-0.7         1966.29        1966         4
-0.6         1966.38        1966         5
0.0         1966.46        1966         6
-0.1         1966.54        1966         7
0.3         1966.63        1966         8
-0.3         1966.71        1966         9
-0.3         1966.79        1966        10
-0.1         1966.88        1966        11
-0.5         1966.96        1966        12

1.5         1967.04        1967         1
1.2         1967.13        1967         2
0.8         1967.21        1967         3
-0.2         1967.29        1967         4
-0.4         1967.38        1967         5
0.6         1967.46        1967         6
0.0         1967.54        1967         7
0.4         1967.63        1967         8
0.5         1967.71        1967         9
-0.2         1967.79        1967        10
-0.7         1967.88        1967        11
-0.7         1967.96        1967        12

0.5         1968.04        1968         1
0.8         1968.13        1968         2
-0.5         1968.21        1968         3
-0.3         1968.29        1968         4
1.2         1968.38        1968         5
1.4         1968.46        1968         6
0.6         1968.54        1968         7
-0.1         1968.63        1968         8
-0.3         1968.71        1968         9
-0.3         1968.79        1968        10
-0.4         1968.88        1968        11
0.0         1968.96        1968        12

-1.4         1969.04        1969         1
0.8         1969.13        1969         2
-0.1         1969.21        1969         3
-0.8         1969.29        1969         4
-0.8         1969.38        1969         5
-0.2         1969.46        1969         6
-0.7         1969.54        1969         7
-0.6         1969.63        1969         8
-1.0         1969.71        1969         9
-1.4         1969.79        1969        10
-0.1         1969.88        1969        11
0.3         1969.96        1969        12

-1.2         1970.04        1970         1
-1.2         1970.13        1970         2
0.0         1970.21        1970         3
-0.5         1970.29        1970         4
0.1         1970.38        1970         5
1.1         1970.46        1970         6
-0.6         1970.54        1970         7
0.3         1970.63        1970         8
1.2         1970.71        1970         9
0.8         1970.79        1970        10
1.8         1970.88        1970        11
1.8         1970.96        1970        12

0.2         1971.04        1971         1
1.4         1971.13        1971         2
2.0         1971.21        1971         3
2.6         1971.29        1971         4
0.9         1971.38        1971         5
0.2         1971.46        1971         6
0.1         1971.54        1971         7
1.4         1971.63        1971         8
1.5         1971.71        1971         9
1.8         1971.79        1971        10
0.5         1971.88        1971        11
0.1         1971.96        1971        12

0.3         1972.04        1972         1
0.6         1972.13        1972         2
0.1         1972.21        1972         3
-0.5         1972.29        1972         4
-2.1         1972.38        1972         5
-1.7         1972.46        1972         6
-1.9         1972.54        1972         7
-1.1         1972.63        1972         8
-1.5         1972.71        1972         9
-1.1         1972.79        1972        10
-0.4         1972.88        1972        11
-1.5         1972.96        1972        12

-0.4         1973.04        1973         1
-1.5         1973.13        1973         2
0.2         1973.21        1973         3
-0.4         1973.29        1973         4
0.3         1973.38        1973         5
1.2         1973.46        1973         6
0.5         1973.54        1973         7
1.2         1973.63        1973         8
1.3         1973.71        1973         9
0.6         1973.79        1973        10
2.9         1973.88        1973        11
1.7         1973.96        1973        12

2.2         1974.04        1974         1
1.5         1974.13        1974         2
2.1         1974.21        1974         3
1.3         1974.29        1974         4
1.3         1974.38        1974         5
0.1         1974.46        1974         6
1.2         1974.54        1974         7
0.5         1974.63        1974         8
1.1         1974.71        1974         9
0.8         1974.79        1974        10
-0.4         1974.88        1974        11
0.0         1974.96        1974        12

-0.6         1975.04        1975         1
0.4         1975.13        1975         2
1.1         1975.21        1975         3
1.5         1975.29        1975         4
0.5         1975.38        1975         5
1.7         1975.46        1975         6
2.1         1975.54        1975         7
2.0         1975.63        1975         8
2.2         1975.71        1975         9
1.7         1975.79        1975        10
1.3         1975.88        1975        11
2.0         1975.96        1975        12

1.2         1976.04        1976         1
1.2         1976.13        1976         2
1.3         1976.21        1976         3
0.2         1976.29        1976         4
0.6         1976.38        1976         5
-0.1         1976.46        1976         6
-1.2         1976.54        1976         7
-1.5         1976.63        1976         8
-1.2         1976.71        1976         9
0.2         1976.79        1976        10
0.7         1976.88        1976        11
-0.5         1976.96        1976        12

-0.5         1977.04        1977         1
0.8         1977.13        1977         2
-1.2         1977.21        1977         3
-1.3         1977.29        1977         4
-1.1         1977.38        1977         5
-2.3         1977.46        1977         6
-1.5         1977.54        1977         7
-1.4         1977.63        1977         8
-0.9         1977.71        1977         9
-1.4         1977.79        1977        10
-1.6         1977.88        1977        11
-1.3         1977.96        1977        12

-0.5         1978.04        1978         1
-2.6         1978.13        1978         2
-0.8         1978.21        1978         3
-0.9         1978.29        1978         4
1.3         1978.38        1978         5
0.4         1978.46        1978         6
0.4         1978.54        1978         7
0.1         1978.63        1978         8
0.0         1978.71        1978         9
-0.8         1978.79        1978        10
-0.1         1978.88        1978        11
-0.2         1978.96        1978        12

-0.5         1979.04        1979         1
0.6         1979.13        1979         2
-0.5         1979.21        1979         3
-0.7         1979.29        1979         4
0.5         1979.38        1979         5
0.6         1979.46        1979         6
1.3         1979.54        1979         7
-0.7         1979.63        1979         8
0.1         1979.71        1979         9
-0.4         1979.79        1979        10
-0.6         1979.88        1979        11
-0.9         1979.96        1979        12

0.3         1980.04        1980         1
0.0         1980.13        1980         2
-1.1         1980.21        1980         3
-1.7         1980.29        1980         4
-0.3         1980.38        1980         5
-0.7         1980.46        1980         6
-0.2         1980.54        1980         7
-0.1         1980.63        1980         8
-0.5         1980.71        1980         9
-0.3         1980.79        1980        10
-0.5         1980.88        1980        11
-0.2         1980.96        1980        12

0.3         1981.04        1981         1
-0.5         1981.13        1981         2
-2.0         1981.21        1981         3
-0.6         1981.29        1981         4
0.8         1981.38        1981         5
1.6         1981.46        1981         6
0.8         1981.54        1981         7
0.4         1981.63        1981         8
0.3         1981.71        1981         9
-0.7         1981.79        1981        10
0.1         1981.88        1981        11
0.4         1981.96        1981        12

1.0         1982.04        1982         1
0.0         1982.13        1982         2
0.0         1982.21        1982         3
-0.1         1982.29        1982         4
-0.6         1982.38        1982         5
-2.5         1982.46        1982         6
-2.0         1982.54        1982         7
-2.7         1982.63        1982         8
-1.9         1982.71        1982         9
-2.2         1982.79        1982        10
-3.2         1982.88        1982        11
-2.5         1982.96        1982        12

-3.4         1983.04        1983         1
-3.5         1983.13        1983         2
-3.2         1983.21        1983         3
-2.1         1983.29        1983         4
0.9         1983.38        1983         5
-0.5         1983.46        1983         6
-0.9         1983.54        1983         7
-0.4         1983.63        1983         8
0.9         1983.71        1983         9
0.3         1983.79        1983        10
-0.1         1983.88        1983        11
-0.1         1983.96        1983        12

0.0         1984.04        1984         1
0.4         1984.13        1984         2
-0.8         1984.21        1984         3
0.4         1984.29        1984         4
0.0         1984.38        1984         5
-1.2         1984.46        1984         6
0.0         1984.54        1984         7
0.1         1984.63        1984         8
0.1         1984.71        1984         9
-0.6         1984.79        1984        10
0.3         1984.88        1984        11
-0.3         1984.96        1984        12

-0.5         1985.04        1985         1
0.8         1985.13        1985         2
0.2         1985.21        1985         3
1.4         1985.29        1985         4
-0.2         1985.38        1985         5
-1.4         1985.46        1985         6
-0.3         1985.54        1985         7
0.7         1985.63        1985         8
0.0         1985.71        1985         9
-0.8         1985.79        1985        10
-0.4         1985.88        1985        11
0.1         1985.96        1985        12

0.8         1986.04        1986         1
-1.2         1986.13        1986         2
-0.1         1986.21        1986         3
0.1         1986.29        1986         4
-0.6         1986.38        1986         5
1.0         1986.46        1986         6
0.1         1986.54        1986         7
-0.9         1986.63        1986         8
-0.5         1986.71        1986         9
0.6         1986.79        1986        10
-1.6         1986.88        1986        11
-1.6         1986.96        1986        12

-0.7         1987.04        1987         1
-1.4         1987.13        1987         2
-2.0         1987.21        1987         3
-2.7         1987.29        1987         4
-2.0         1987.38        1987         5
-2.7         1987.46        1987         6
-1.8         1987.54        1987         7
-1.7         1987.63        1987         8
-1.1         1987.71        1987         9
-0.7         1987.79        1987        10
-0.1         1987.88        1987        11
-0.6         1987.96        1987        12

-0.3         1988.04        1988         1
-0.6         1988.13        1988         2
0.1         1988.21        1988         3
0.0         1988.29        1988         4
1.1         1988.38        1988         5
-0.3         1988.46        1988         6
1.1         1988.54        1988         7
1.4         1988.63        1988         8
1.9         1988.71        1988         9
1.5         1988.79        1988        10
1.9         1988.88        1988        11
1.1         1988.96        1988        12

1.5         1989.04        1989         1
1.1         1989.13        1989         2
0.6         1989.21        1989         3
1.6         1989.29        1989         4
1.2         1989.38        1989         5
0.5         1989.46        1989         6
0.8         1989.54        1989         7
-0.8         1989.63        1989         8
0.6         1989.71        1989         9
0.6         1989.79        1989        10
-0.4         1989.88        1989        11
-0.7         1989.96        1989        12

-0.2         1990.04        1990         1
-2.4         1990.13        1990         2
-1.2         1990.21        1990         3
0.0         1990.29        1990         4
1.1         1990.38        1990         5
0.0         1990.46        1990         6
0.5         1990.54        1990         7
-0.5         1990.63        1990         8
-0.8         1990.71        1990         9
0.1         1990.79        1990        10
-0.7         1990.88        1990        11
-0.4         1990.96        1990        12

0.6         1991.04        1991         1
-0.1         1991.13        1991         2
-1.4         1991.21        1991         3
-1.0         1991.29        1991         4
-1.5         1991.38        1991         5
-0.5         1991.46        1991         6
-0.2         1991.54        1991         7
-0.9         1991.63        1991         8
-1.8         1991.71        1991         9
-1.5         1991.79        1991        10
-0.8         1991.88        1991        11
-2.3         1991.96        1991        12

-3.4         1992.04        1992         1
-1.4         1992.13        1992         2
-3.0         1992.21        1992         3
-1.4         1992.29        1992         4
0.0         1992.38        1992         5
-1.2         1992.46        1992         6
-0.8         1992.54        1992         7
0.0         1992.63        1992         8
0.0         1992.71        1992         9
-1.9         1992.79        1992        10
-0.9         1992.88        1992        11
-1.1         1992.96        1992        12

```