nyabs=read.csv("ACTUARIAL.CSV");nyabs
##        TIME   CPI PENSION Year     Month INFLATION CLAIMS
## 1   2007-01  6.12   13.50 2018  November      5.58   4.59
## 2   2007-02  6.33   13.59 2018   October      5.53   4.53
## 3   2007-03  6.47   13.49 2018 September      5.70   4.53
## 4   2007-04  6.48   13.47 2018    August      4.04   4.63
## 5   2007-05  6.51   13.70 2018      July      4.35   4.95
## 6   2007-06  6.56   13.73 2018      June      4.28   5.20
## 7   2007-07  6.57   13.71 2018       May      3.95   5.61
## 8   2007-08  6.64   13.83 2018     April      3.73   6.24
## 9   2007-09  6.66   13.85 2018     March      4.18   6.89
## 10  2007-10  6.68   13.76 2018  February      4.46   7.40
## 11  2007-11  6.68   13.66 2018   January      4.83   7.79
## 12  2007-12  6.81   13.65 2017  December      4.50   7.98
## 13  2008-01  7.06   13.61 2017  November      4.73   8.15
## 14  2008-02  7.16   13.61 2017   October      5.72   8.33
## 15  2008-03  7.19   13.81 2017 September      7.06   8.40
## 16  2008-04  7.19   14.23 2017    August      8.04   8.36
## 17  2008-05  7.20   14.29 2017      July      7.47   8.21
## 18  2008-06  7.25   14.39 2017      June      9.21   8.13
## 19  2008-07  7.23   14.24 2017       May     11.70   7.84
## 20  2008-08  7.25   14.25 2017     April     11.48   7.20
## 21  2008-09  7.27   14.45 2017     March     10.28   6.76
## 22  2008-10  7.33   15.32 2017  February      9.04   6.43
## 23  2008-11  7.36   15.49 2017   January      6.99   6.26
## 24  2008-12  7.46   17.28 2016  December      6.35   6.30
## 25  2009-01  7.62   18.47 2016  November      6.68   6.43
## 26  2009-02  7.72   22.51 2016   October      6.47   6.48
## 27  2009-03  7.75   23.03 2016 September      6.34   6.50
## 28  2009-04  7.77   23.04 2016    August      6.26   6.47
## 29  2009-05  7.78   23.43 2016      July      6.40   6.44
## 30  2009-06  7.86   22.36 2016      June      5.80   6.46
## 31  2009-07  7.87   23.27 2016       May      5.00   6.59
## 32  2009-08  7.88   20.84 2016     April      5.27   6.72
## 33  2009-09  7.95   19.98 2016     March      6.45   6.88
## 34  2009-10  8.02   18.61 2016  February      6.84   6.87
## 35  2009-11  8.06   17.76 2016   January      7.78   6.77
## 36  2009-12  8.21   17.42 2015  December      8.01   6.58
## 37  2010-01  8.41   16.69 2015  November      7.32   6.42
## 38  2010-02  8.43   16.67 2015   October      6.72   6.31
## 39  2010-03  8.60   16.76 2015 September      5.97   6.29
## 40  2010-04  8.66   15.11 2015    August      5.84   6.34
## 41  2010-05  8.69   14.05 2015      July      6.62   6.54
## 42  2010-06  8.83   13.05 2015      June      7.03   6.63
## 43  2010-07  8.84   12.20 2015       May      6.87   6.65
## 44  2010-08  8.96   12.08 2015     April      7.08   6.69
## 45  2010-09  9.13   11.30 2015     March      6.31   6.63
## 46  2010-10  9.16   10.83 2015  February      5.61   6.63
## 47  2010-11  9.19    9.81 2015   January      5.53   6.74
## 48  2010-12  9.28   10.13 2014  December      6.02   6.88
## 49  2011-01  9.57   10.32 2014  November      6.09   6.97
## 50  2011-02  9.60   11.90 2014   October      6.43   7.08
## 51  2011-03  9.76   11.80 2014 September      6.60   7.19
## 52  2011-04  9.85   11.97 2014    August      8.36   7.33
## 53  2011-05  9.92   12.46 2014      July      7.67   7.19
## 54  2011-06 10.06   12.77 2014      June      7.39   7.05
## 55  2011-07 10.16   13.33 2014       May      7.30   6.85
## 56  2011-08 10.11   13.62 2014     April      6.41   6.58
## 57  2011-09 10.23   13.89 2014     March      6.27   6.39
## 58  2011-10 10.28   14.23 2014  February      6.86   6.21
## 59  2011-11 10.34   14.19 2014   January      7.21   6.01
## 60  2011-12 10.54   14.17 2013  December      7.15   5.72
## 61  2012-01 10.92   14.05 2013  November      7.36   5.39
## 62  2012-02 10.96   13.90 2013   October      7.76   5.05
## 63  2012-03 11.17   14.28 2013 September      8.29   4.75
## 64  2012-04 11.32   14.19 2013    August      6.67   4.50
## 65  2012-05 11.28   14.29 2013      July      6.03   4.44
## 66  2012-06 11.43   14.65 2013      June      4.91   4.56
## 67  2012-07 11.46   14.54 2013       May      4.05   4.96
## 68  2012-08 11.49   14.47 2013     April      4.14   5.61
## 69  2012-09 11.77   14.33 2013     March      4.11   6.33
## 70  2012-10 12.18   14.24 2013  February      4.45   7.24
## 71  2012-11 12.47   14.95 2013   January      3.67   8.20
## 72  2012-12 12.79   13.89 2012  December      3.20   9.38
## 73  2013-01 12.73   14.11 2012  November      3.25  10.67
## 74  2013-02 13.07   14.06 2012   October      4.14  12.04
## 75  2013-03 13.31   14.53 2012 September      5.32  13.29
## 76  2013-04 13.32   15.21 2012    August      6.09  14.33
## 77  2013-05 13.67   15.88 2012      July      7.74  15.27
## 78  2013-06 13.79   16.02 2012      June     10.05  15.97
## 79  2013-07 13.96   15.94 2012       May     12.22  16.40
## 80  2013-08 14.01   15.88 2012     April     13.06  16.50
## 81  2013-09 14.38   15.89 2012     March     15.61  16.45
## 82  2013-10 14.40   18.37 2012  February     16.69  15.93
## 83  2013-11 14.48   17.85 2012   January     18.31  15.10
## 84  2013-12 14.56   16.87 2011  December     18.93  14.02
## 85  2014-01 14.83   16.67 2011  November     19.72  12.82
## 86  2014-02 14.97   16.35 2011   October     18.91  11.49
## 87  2014-03 16.27   15.96 2011 September     17.32  10.18
## 88  2014-04 16.40   15.39 2011    August     16.67   9.00
## 89  2014-05 16.94   14.67 2011      July     15.53   7.88
## 90  2014-06 18.68   12.99 2011      June     14.48   6.88
## 91  2014-07 18.46   11.25 2011       May     12.95   5.96
## 92  2014-08 18.54    9.66 2011     April     12.05   5.20
## 93  2014-09 18.85    8.93 2011     March      9.19   4.49
## 94  2014-10 18.62    8.18 2011  February      6.54   4.05
## 95  2014-11 18.92    7.55 2011   January      5.42   3.93
## 96  2014-12 19.46    7.83 2010  December      4.51   3.96
## 97  2015-01 19.59    7.65 2010  November      3.84   4.02
## 98  2015-02 21.16    7.79 2010   October      3.18   4.12
## 99  2015-03 21.83    8.44 2010 September      3.21   4.40
## 100 2015-04 23.31    9.10 2010    August      3.22   4.69
## 101 2015-05 24.16    9.48 2010      July      3.57   5.03
## 102 2015-06 25.99    9.74 2010      June      3.49   5.43
## 103 2015-07 26.47   10.38 2010       May      3.88   5.85
## 104 2015-08 27.38    9.17 2010     April      3.66   6.32
## 105 2015-09 29.02    8.01 2010     March      3.97   7.03
## 106 2015-10 29.32    7.61 2010  February      5.18   7.88
## 107 2015-11 29.63    7.21 2010   January      5.95   8.64
## 108 2015-12 30.11    7.01 2009  December      5.32   9.24
## 109 2016-01 31.64    6.67 2009  November      5.00  10.24
## 110 2016-02 32.65    6.26 2009   October      6.62  11.42
## 111 2016-03 33.54    6.22 2009 September      6.74  12.41
## 112 2016-04 34.44    6.22 2009    August      7.36  13.42
## 113 2016-05 34.09    6.20 2009      July      8.44  14.35
## 114 2016-06 33.46    6.22 2009      June      8.60  15.11
## 115 2016-07 33.70    6.54 2009       May      9.61  15.93
## 116 2016-08 33.26    6.55 2009     April     12.42  16.72
## 117 2016-09 32.75    6.92 2009     March     14.60  17.07
## 118 2016-10 32.92    6.58 2009  February     14.69  16.87
## 119 2016-11 32.12    6.44 2009   January     13.22  16.56
## 120 2016-12 32.10    6.36 2008  December     17.83  16.27
## 121 2017-01 32.77    6.22 2008  November     19.54  15.25
## 122 2017-02 33.11    6.24 2008   October     18.74  14.13
## 123 2017-03 33.31    6.27 2008 September     18.73  13.02
## 124 2017-04 33.18    6.21 2008    August     18.33  11.92
## 125 2017-05 33.46    5.87 2008      July     17.12  10.83
## 126 2017-06 33.51    5.70 2008      June     17.87   9.86
## 127 2017-07 33.52    5.72 2008       May     18.61   8.70
## 128 2017-08 33.70    5.52 2008     April     16.12   7.32
## 129 2017-09 34.06    5.42 2008     March     11.90   6.13
## 130 2017-10 34.00    5.48 2008  February     10.58   5.32
## 131 2017-11 33.90    5.31 2008   January      9.40   4.69
## 132 2017-12 34.31    5.21 2007  December      5.70   4.27
## 133 2018-01 34.71    5.08 2007  November      6.08   4.45
## 134 2018-02 34.88    4.99 2007   October      5.38   4.48
## 135 2018-03 35.44    4.80 2007 September      5.53   4.57
## 136 2018-04 35.56    4.66 2007    August      5.30   4.60
## 137 2018-05 35.80    4.75 2007      July      5.48   4.57
## 138 2018-06 36.73    4.75 2007      June      4.07   4.46
## 139 2018-06 37.23    4.68 2007       May      1.96   4.47
## 140            NA      NA 2007     April      1.85   4.69
## 141            NA      NA 2007     March      2.19   4.99
## 142            NA      NA 2007  February      3.02   5.55
## 143            NA      NA 2007   January      4.63   6.08
## 144            NA      NA 2006  December      7.98   6.39
## 145            NA      NA 2006  November      6.64   6.12
## 146            NA      NA 2006   October      6.55   5.94
## 147            NA      NA 2006 September      5.93   5.70
## 148            NA      NA 2006    August      4.92   5.57
## 149            NA      NA 2006      July      4.16   5.73
## 150            NA      NA 2006      June      4.28   6.33
## 151            NA      NA 2006       May      4.47   6.95
## 152            NA      NA 2006     April      5.44   7.77
## 153            NA      NA 2006     March      8.85   8.61
## 154            NA      NA 2006  February      9.39   9.01
## 155            NA      NA 2006   January      8.39   9.36
## 156            NA      NA 2005  December      4.70   9.87
## 157            NA      NA 2005  November      4.40  10.89
## 158            NA      NA 2005   October      3.72  11.99
## 159            NA      NA 2005 September      4.27  13.24
## 160            NA      NA 2005    August      6.87  14.53
## 161            NA      NA 2005      July     11.76  15.34
## 162            NA      NA 2005      June     11.92  15.10
## 163            NA      NA 2005       May     14.78  14.61
## 164            NA      NA 2005     April     16.02  13.76
## 165            NA      NA 2005     March     14.15  13.07
## 166            NA      NA 2005  February     13.94  12.60
## 167            NA      NA 2005   January     14.87  12.27
myd=nyabs$INFLATION;myd
##   [1]  5.58  5.53  5.70  4.04  4.35  4.28  3.95  3.73  4.18  4.46  4.83  4.50
##  [13]  4.73  5.72  7.06  8.04  7.47  9.21 11.70 11.48 10.28  9.04  6.99  6.35
##  [25]  6.68  6.47  6.34  6.26  6.40  5.80  5.00  5.27  6.45  6.84  7.78  8.01
##  [37]  7.32  6.72  5.97  5.84  6.62  7.03  6.87  7.08  6.31  5.61  5.53  6.02
##  [49]  6.09  6.43  6.60  8.36  7.67  7.39  7.30  6.41  6.27  6.86  7.21  7.15
##  [61]  7.36  7.76  8.29  6.67  6.03  4.91  4.05  4.14  4.11  4.45  3.67  3.20
##  [73]  3.25  4.14  5.32  6.09  7.74 10.05 12.22 13.06 15.61 16.69 18.31 18.93
##  [85] 19.72 18.91 17.32 16.67 15.53 14.48 12.95 12.05  9.19  6.54  5.42  4.51
##  [97]  3.84  3.18  3.21  3.22  3.57  3.49  3.88  3.66  3.97  5.18  5.95  5.32
## [109]  5.00  6.62  6.74  7.36  8.44  8.60  9.61 12.42 14.60 14.69 13.22 17.83
## [121] 19.54 18.74 18.73 18.33 17.12 17.87 18.61 16.12 11.90 10.58  9.40  5.70
## [133]  6.08  5.38  5.53  5.30  5.48  4.07  1.96  1.85  2.19  3.02  4.63  7.98
## [145]  6.64  6.55  5.93  4.92  4.16  4.28  4.47  5.44  8.85  9.39  8.39  4.70
## [157]  4.40  3.72  4.27  6.87 11.76 11.92 14.78 16.02 14.15 13.94 14.87
library(fGarch)
## Warning: package 'fGarch' was built under R version 4.3.3
## NOTE: Packages 'fBasics', 'timeDate', and 'timeSeries' are no longer
## attached to the search() path when 'fGarch' is attached.
## 
## If needed attach them yourself in your R script by e.g.,
##         require("timeSeries")
log.INT=diff(myd);log.INT
##   [1] -0.05  0.17 -1.66  0.31 -0.07 -0.33 -0.22  0.45  0.28  0.37 -0.33  0.23
##  [13]  0.99  1.34  0.98 -0.57  1.74  2.49 -0.22 -1.20 -1.24 -2.05 -0.64  0.33
##  [25] -0.21 -0.13 -0.08  0.14 -0.60 -0.80  0.27  1.18  0.39  0.94  0.23 -0.69
##  [37] -0.60 -0.75 -0.13  0.78  0.41 -0.16  0.21 -0.77 -0.70 -0.08  0.49  0.07
##  [49]  0.34  0.17  1.76 -0.69 -0.28 -0.09 -0.89 -0.14  0.59  0.35 -0.06  0.21
##  [61]  0.40  0.53 -1.62 -0.64 -1.12 -0.86  0.09 -0.03  0.34 -0.78 -0.47  0.05
##  [73]  0.89  1.18  0.77  1.65  2.31  2.17  0.84  2.55  1.08  1.62  0.62  0.79
##  [85] -0.81 -1.59 -0.65 -1.14 -1.05 -1.53 -0.90 -2.86 -2.65 -1.12 -0.91 -0.67
##  [97] -0.66  0.03  0.01  0.35 -0.08  0.39 -0.22  0.31  1.21  0.77 -0.63 -0.32
## [109]  1.62  0.12  0.62  1.08  0.16  1.01  2.81  2.18  0.09 -1.47  4.61  1.71
## [121] -0.80 -0.01 -0.40 -1.21  0.75  0.74 -2.49 -4.22 -1.32 -1.18 -3.70  0.38
## [133] -0.70  0.15 -0.23  0.18 -1.41 -2.11 -0.11  0.34  0.83  1.61  3.35 -1.34
## [145] -0.09 -0.62 -1.01 -0.76  0.12  0.19  0.97  3.41  0.54 -1.00 -3.69 -0.30
## [157] -0.68  0.55  2.60  4.89  0.16  2.86  1.24 -1.87 -0.21  0.93
ts.plot(log.INT)

summary(log.INT)
##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
## -4.22000 -0.68750  0.04000  0.05596  0.62000  4.89000

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