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I am trying to fit an arima model to data below. The best model seems to be ARMA(2,2) with the first AR and MA components zero to me. However, it does not quite satisfy me. I am looking for any ideas to lead me to a better model. Data plot, acf, pacf and fitted model results are below

  [1]  3.800731572  1.964861846 -0.330186755 -2.074280974  0.045544766  1.414932643
  [7] -1.772733971 -0.269238758  2.201851709 -0.923099841 -2.022964462  1.244593286
 [13]  0.138510229  0.207393784 -1.179208337 -2.600458137  1.597338790  2.672883672
 [19]  0.021512541 -0.239735960 -0.241002298 -2.652076605 -1.006429172  4.069421128
 [25]  1.567593649 -3.809127815 -1.098172055  0.461986823 -0.371368587  2.377791538
 [31] -0.343117083 -1.627939880 -1.495075368  1.089181437  0.559939059 -1.628253076
 [37]  2.110155105  1.016467745 -2.427617328  1.244370318  0.964439525 -1.102202024
 [43]  0.165851643 -0.229573936 -1.624649814  0.295206971  0.068025881 -1.134450650
 [49] -0.028201597  2.503538284  1.114222419 -2.833496083 -0.522543695  0.050113179
 [55]  0.125369098  2.105797843  2.830923699 -4.856194214 -3.273881724  3.279800792
 [61]  2.239616685 -0.908085837  0.139333522 -1.450735818 -0.803266180  2.190218597
 [67]  1.173394051 -1.246471581  1.242838802  0.072678970 -2.275862413 -0.107232220
 [73] -0.536815960 -0.194192692  4.280008694 -0.434172239 -4.423742767 -0.086640065
 [79]  1.953905466  0.980978972  0.718926929 -2.118235181 -3.086168990  3.488865741
 [85]  3.599936662 -3.739336414 -0.543348582  0.301020550 -1.055976766  2.578110734
 [91]  1.595147532 -1.380082733 -1.554146884  1.611852730 -0.024437323 -0.695824440
 [97]  1.212412282 -0.905360495 -1.731530168  0.175207750  2.228134579 -0.249534514
[103]  0.317061339  0.301498249 -2.915450651  0.700227471  4.178040621  0.300634992
[109] -2.775388196 -0.813531442  1.682700373  0.170627572 -0.304814504  0.593898664
[115]  0.705283783  0.247763384 -0.973869829  0.797997103 -0.210376025 -0.664768398
[121]  0.007792289 -0.123965987 -1.053204162  1.317299536  3.605380859 -0.207812137
[127] -2.753767618 -0.953270567  1.302774452  0.475310161  0.439760253 -0.519127147
[133] -2.713290201  0.528059101  1.590144928  0.290186322 -1.140784855 -0.290639801
[139]  0.451966832 -1.829276852  0.616356479  3.382008422 -0.372334534  0.586538986
[145]  1.065393107 -1.045478951 -1.297666091 -0.804821865 -0.894058890  0.945981384
[151]  1.865434286 -2.347928952 -1.145754072  4.593493727 -0.509447663 -1.593344586
[157]  0.161678089 -1.102974728  1.219269299  2.142194154 -2.169974430 -0.847790444
[163]  2.112060982 -1.994966429 -1.549014700  2.163255646 -0.794707401 -0.255578617
[169]  1.691674982 -0.901877878 -0.336901862  2.345808096 -1.869011631  0.415512418
[175]  1.417162468 -0.189171118  0.604161930 -2.354043433 -3.087017949  1.391578651
[181]  1.607888511 -2.601455766  1.653942000  1.040655043 -2.547348811 -0.811884895
[187]  1.291304418  1.346237124  0.646396579 -0.888786433 -1.238057892 -0.801669576
[193]  0.360090751  0.751050406  0.273321234 -0.919838506 -0.791943921  1.771953858
[199] -0.306807634 -1.033265249 

enter image description here

acf enter image description here

ARIMA(2,0,2) with non-zero mean 

Coefficients:
      ar1      ar2  ma1      ma2  intercept
        0  -0.3677    0  -0.6407    -0.0044
s.e.    0   0.0767    0   0.0536     0.0222

sigma^2 estimated as 1.366:  log likelihood=-316.07
AIC=638.14   AICc=638.57   BIC=657.93
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  • $\begingroup$ You say you include fitted model results. Where are they? $\endgroup$ – Glen_b -Reinstate Monica May 11 '14 at 23:05
  • $\begingroup$ I put them now. Sorry for inconveniance $\endgroup$ – arke May 11 '14 at 23:07
  • $\begingroup$ Is the "(0,NA,0,NA)" part simply specifying that the first AR and MA components are zero? $\endgroup$ – Glen_b -Reinstate Monica May 11 '14 at 23:14
  • $\begingroup$ yes,it is the notation in R $\endgroup$ – arke May 11 '14 at 23:21
  • $\begingroup$ Anybody who doesn't use time series in R is unlikely to guess its meaning, so you must make it explicit what you mean in the question; I'd suggest replacing (0,NA,0,NA) with a sentence explaining that you have set the specific coefficients to zero. $\endgroup$ – Glen_b -Reinstate Monica May 11 '14 at 23:27

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