[R] subject: Log likelihood above 0

[Daniel Haugstvedt]

Hi -

In an effort to learn some basic arima modeling in R i went through
the tutorial found at
http://www.stat.pitt.edu/stoffer/tsa2/R_time_series_quick_fix.htm

One of the examples gave me a log likelihood of 77. Now I am simply
wondering if this is the expected behavior? Looking in my text book
this should not be possible. I have actually spent some time on this
but neither the documentation ?arima or google gave me a satisfying
answer.



Data and code:

gTemp.raw = c(-0.11, -0.13, -0.01, -0.04, -0.42, -0.23, -0.25, -0.45,
-0.23, 0.04, -0.22, -0.55
, -0.40,  -0.39, -0.32, -0.32, -0.27, -0.15, -0.21, -0.25, -0.05,
-0.05, -0.30, -0.35
, -0.42,  -0.25, -0.15, -0.41, -0.30, -0.31, -0.21, -0.25, -0.33,
-0.28, -0.02,  0.06
, -0.20,  -0.46, -0.33, -0.09, -0.15, -0.04, -0.09, -0.16, -0.11,
-0.15,  0.04, -0.05
,  0.01,  -0.22, -0.03,  0.03,  0.04, -0.11,  0.05, -0.08,  0.01,
0.12,  0.15, -0.02
,  0.14,   0.11,  0.10,  0.06,  0.10, -0.01,  0.01,  0.12, -0.03,
-0.09, -0.17, -0.02
,  0.03,   0.12, -0.09, -0.09, -0.18,  0.08,  0.10,  0.05, -0.02,
0.10,  0.05,  0.03
, -0.25,  -0.15, -0.07, -0.02, -0.09,  0.00,  0.04, -0.10, -0.05,
0.18, -0.06, -0.02
, -0.21,   0.16,  0.07,  0.13,  0.27,  0.40,  0.10,  0.34,  0.16,
0.13,  0.19,  0.35
,  0.42,   0.28,  0.49,  0.44,  0.16,  0.18,  0.31,  0.47,  0.36,
0.40,  0.71,  0.43
,  0.41,   0.56,  0.70,  0.66,  0.60)

gTemp.ts = ts(gTemp.raw, start=1880, freq=1)

gTemp.model = arima(diff(gTemp.ts), order=c(1,0,1))



Results:

> gTemp.model

Call:
arima(x = diff(gTemp.ts), order = c(1, 0, 1))

Coefficients:
         ar1      ma1         intercept
       0.2695  -0.8180     0.0061
s.e.  0.1122   0.0624     0.0030

sigma^2 estimated as 0.01680:  log likelihood = 77.05,  aic = -146.11