# Arma model fitting

#### arke9

##### New Member
Below is my data. Only lag 2 is significant in both pacf and acf plot.EACF says it is ARMA(0,2) and I think it can be. However,if it is, aren't there supposed to be tailing off in PACF and significant both 1 and 2 lag.
I put some plots and model fitting result below. I am waiting for your advices.Thanks is adavance

[1] -0.85207456 0.09379796 0.52695975 1.14152956 -0.54953897 -2.31203123
[7] 1.91749080 1.17457890 -0.17572130 -1.14985960 -0.07667550 -1.51952760
[13] -0.92170680 1.17750180 0.78119110 -2.51962010 -0.31687070 0.32149010
[19] 0.69775340 -0.25110750 -2.44269180 -2.46347950 0.10528280 0.35101500
[25] -1.42027650 -0.53951670 -0.66747520 -0.63354000 0.23501390 0.34057669
[31] -0.23008191 3.42378310 -1.46940363 -1.41753955 0.44807250 0.81785214
[37] 2.38783968 0.13809092 -0.60939463 -1.42044282 -0.37067105 0.31711685
[43] -1.33107090 0.17284619 1.83866858 -0.36720704 -1.09616594 -1.03752229
[49] 0.09685998 1.19676159 0.15660898 -0.71783903 -0.41122892 -2.60209345
[55] -0.35285255 2.62925018 1.19647676 -0.48616539 -2.23894555 -0.06738858
[61] 0.66619905 0.54312951 -0.35422437 -0.48879011 -0.87327397 -0.43265791
[67] -1.59057630 -0.36481867 0.42942336 -0.41530310 -0.40149760 0.92997520
[73] -0.05847810 0.62459520 0.14449990 -0.85027890 1.30673650 1.07664030
[79] 0.11346480 -0.09452350 -0.88274090 -1.34218230 -0.42007390 0.94168890
[85] 1.24777670 -0.19239250 -0.56253830 -1.11826540 -1.64875860 0.37494000
[91] 0.49316920 0.09744480 -0.50955100 -1.38922150 -0.04084500 1.83572430
[97] -0.43371890 -0.63572840 -0.18488360 -0.00018490 0.16986960 0.93785310
[103] -0.41355490 -0.61605680 1.11373090 0.67697250 -1.52931440 0.44433230
[109] -0.21807400 -2.12619500 -0.98259410 1.03158840 -0.16715930 -1.64628300
[115] 0.70783870 0.37037870 -0.84197970 0.50856150 -0.02340410 -0.55127050
[121] -1.12226900 0.07828340 0.62803650 1.15856500 1.61352170 0.76287230
[127] 0.90832340 1.06233180 0.55230020 -0.79271900 -2.10460870 1.32085210
[133] 1.23814720 -0.37765640 1.07114070 0.97610140 -1.48502580 -1.57002320
[139] 0.12029180 0.83748290 0.69661110 0.72453420 -1.91443880 0.01681360
[145] 1.94435380 -0.69977300 -1.41016160 1.00647380 0.75173770 -0.21908960
[151] -0.39167110 -0.67189810 -0.27100090 2.13059010 1.01513400 -0.74648300
[157] -0.67913600 -1.38164300 1.24767600 -0.88297700 -2.20870300 0.70367200
[163] 2.75550300 0.01835500 -0.46490400 2.31346600 -0.06412100 -0.85937200
[169] -0.79275800 -1.33250000 0.19584500 -1.84150000 -0.37637400 -0.87623400
[175] -0.57995900 -0.19078200 -0.47503000 -0.50371300 -0.84934400 -0.79262700
[181] -0.46782200 0.15708900 1.74542600 -0.52995900 -0.69511000 0.22369800
[187] 0.36030800 -0.05169900 2.32600600 0.20539500 -0.03064800 0.90829400
[193] -0.20459600 0.01366800 1.31014600 -0.84247900 0.33095500 1.25819600

arima(x = mydata, order = c(0, 2, 2))

Coefficients:
ma1 ma2
0.1936 -0.327
s.e. 0.0652 0.061

sigma^2 estimated as 0.9952: log likelihood = -280.63, aic = 565.26

arima(x = mydata, order = c(0, 2, 2), fixed = c(0, NA))

Coefficients:
ma1 ma2
0 -0.3204
s.e. 0 0.0601

sigma^2 estimated as 1.041: log likelihood = -285.03, aic = 572.05

#### noetsi

##### Fortran must die
Is the data differenced? If so it should not be a (0,2) ARMA, it should be an ARIMA model with an order of differencing. Regardless of that point if you have a sharp spike at both PACF and ACF of 2 it suggest a mixed model to me. Possibly a (2,2) although you might try a (1,1) model and see if that reduces the patterns to white noise (box-ljung test are useful for that analysis).