MTH6139 Time Series Coursework 1

Meta’s Prophet Forcasting System

1 Purpose

We are going to explore 2 time series using Meta’s Prophet forecasting system.It is a tool that would make accurate prediction on future values in any time series data using a simple parameters. It is fast,easy and can handle with any errors such as missing values.It can be modelled in weeks, months or years and depends on trends, seasonality, holiday and error.

2 Mauna Lou Atmospheric CO2 Concentration

One of the largest active volcano in Hawaii

2.1 Introduction

Manua Loa is an active and shield volcano in the US state of Hawaii. It is one of the largest volcano by both mass and volume- which is 75000 cubic kilometre. It records how much atmospheric concentrations of CO2 are released from Mauna Loa in parts per million (ppm). It is already stored in R as ‘co2’ A time series of 468 observations is recorded from 1959 to 1997 and is recorded monthly. However, there are few observations from 1964 is missing and therefore is obtained by interpolation.

2.2 Data

This is the dataset of 468 observations of how much CO2 concentration are expressed.

dataFrame = data.frame(ds=zoo::as.yearmon(time(co2)),y=co2)#Creating this time series into data frame
dataFrame

##           ds      y
## 1   Jan 1959 315.42
## 2   Feb 1959 316.31
## 3   Mar 1959 316.50
## 4   Apr 1959 317.56
## 5   May 1959 318.13
## 6   Jun 1959 318.00
## 7   Jul 1959 316.39
## 8   Aug 1959 314.65
## 9   Sep 1959 313.68
## 10  Oct 1959 313.18
## 11  Nov 1959 314.66
## 12  Dec 1959 315.43
## 13  Jan 1960 316.27
## 14  Feb 1960 316.81
## 15  Mar 1960 317.42
## 16  Apr 1960 318.87
## 17  May 1960 319.87
## 18  Jun 1960 319.43
## 19  Jul 1960 318.01
## 20  Aug 1960 315.74
## 21  Sep 1960 314.00
## 22  Oct 1960 313.68
## 23  Nov 1960 314.84
## 24  Dec 1960 316.03
## 25  Jan 1961 316.73
## 26  Feb 1961 317.54
## 27  Mar 1961 318.38
## 28  Apr 1961 319.31
## 29  May 1961 320.42
## 30  Jun 1961 319.61
## 31  Jul 1961 318.42
## 32  Aug 1961 316.63
## 33  Sep 1961 314.83
## 34  Oct 1961 315.16
## 35  Nov 1961 315.94
## 36  Dec 1961 316.85
## 37  Jan 1962 317.78
## 38  Feb 1962 318.40
## 39  Mar 1962 319.53
## 40  Apr 1962 320.42
## 41  May 1962 320.85
## 42  Jun 1962 320.45
## 43  Jul 1962 319.45
## 44  Aug 1962 317.25
## 45  Sep 1962 316.11
## 46  Oct 1962 315.27
## 47  Nov 1962 316.53
## 48  Dec 1962 317.53
## 49  Jan 1963 318.58
## 50  Feb 1963 318.92
## 51  Mar 1963 319.70
## 52  Apr 1963 321.22
## 53  May 1963 322.08
## 54  Jun 1963 321.31
## 55  Jul 1963 319.58
## 56  Aug 1963 317.61
## 57  Sep 1963 316.05
## 58  Oct 1963 315.83
## 59  Nov 1963 316.91
## 60  Dec 1963 318.20
## 61  Jan 1964 319.41
## 62  Feb 1964 320.07
## 63  Mar 1964 320.74
## 64  Apr 1964 321.40
## 65  May 1964 322.06
## 66  Jun 1964 321.73
## 67  Jul 1964 320.27
## 68  Aug 1964 318.54
## 69  Sep 1964 316.54
## 70  Oct 1964 316.71
## 71  Nov 1964 317.53
## 72  Dec 1964 318.55
## 73  Jan 1965 319.27
## 74  Feb 1965 320.28
## 75  Mar 1965 320.73
## 76  Apr 1965 321.97
## 77  May 1965 322.00
## 78  Jun 1965 321.71
## 79  Jul 1965 321.05
## 80  Aug 1965 318.71
## 81  Sep 1965 317.66
## 82  Oct 1965 317.14
## 83  Nov 1965 318.70
## 84  Dec 1965 319.25
## 85  Jan 1966 320.46
## 86  Feb 1966 321.43
## 87  Mar 1966 322.23
## 88  Apr 1966 323.54
## 89  May 1966 323.91
## 90  Jun 1966 323.59
## 91  Jul 1966 322.24
## 92  Aug 1966 320.20
## 93  Sep 1966 318.48
## 94  Oct 1966 317.94
## 95  Nov 1966 319.63
## 96  Dec 1966 320.87
## 97  Jan 1967 322.17
## 98  Feb 1967 322.34
## 99  Mar 1967 322.88
## 100 Apr 1967 324.25
## 101 May 1967 324.83
## 102 Jun 1967 323.93
## 103 Jul 1967 322.38
## 104 Aug 1967 320.76
## 105 Sep 1967 319.10
## 106 Oct 1967 319.24
## 107 Nov 1967 320.56
## 108 Dec 1967 321.80
## 109 Jan 1968 322.40
## 110 Feb 1968 322.99
## 111 Mar 1968 323.73
## 112 Apr 1968 324.86
## 113 May 1968 325.40
## 114 Jun 1968 325.20
## 115 Jul 1968 323.98
## 116 Aug 1968 321.95
## 117 Sep 1968 320.18
## 118 Oct 1968 320.09
## 119 Nov 1968 321.16
## 120 Dec 1968 322.74
## 121 Jan 1969 323.83
## 122 Feb 1969 324.26
## 123 Mar 1969 325.47
## 124 Apr 1969 326.50
## 125 May 1969 327.21
## 126 Jun 1969 326.54
## 127 Jul 1969 325.72
## 128 Aug 1969 323.50
## 129 Sep 1969 322.22
## 130 Oct 1969 321.62
## 131 Nov 1969 322.69
## 132 Dec 1969 323.95
## 133 Jan 1970 324.89
## 134 Feb 1970 325.82
## 135 Mar 1970 326.77
## 136 Apr 1970 327.97
## 137 May 1970 327.91
## 138 Jun 1970 327.50
## 139 Jul 1970 326.18
## 140 Aug 1970 324.53
## 141 Sep 1970 322.93
## 142 Oct 1970 322.90
## 143 Nov 1970 323.85
## 144 Dec 1970 324.96
## 145 Jan 1971 326.01
## 146 Feb 1971 326.51
## 147 Mar 1971 327.01
## 148 Apr 1971 327.62
## 149 May 1971 328.76
## 150 Jun 1971 328.40
## 151 Jul 1971 327.20
## 152 Aug 1971 325.27
## 153 Sep 1971 323.20
## 154 Oct 1971 323.40
## 155 Nov 1971 324.63
## 156 Dec 1971 325.85
## 157 Jan 1972 326.60
## 158 Feb 1972 327.47
## 159 Mar 1972 327.58
## 160 Apr 1972 329.56
## 161 May 1972 329.90
## 162 Jun 1972 328.92
## 163 Jul 1972 327.88
## 164 Aug 1972 326.16
## 165 Sep 1972 324.68
## 166 Oct 1972 325.04
## 167 Nov 1972 326.34
## 168 Dec 1972 327.39
## 169 Jan 1973 328.37
## 170 Feb 1973 329.40
## 171 Mar 1973 330.14
## 172 Apr 1973 331.33
## 173 May 1973 332.31
## 174 Jun 1973 331.90
## 175 Jul 1973 330.70
## 176 Aug 1973 329.15
## 177 Sep 1973 327.35
## 178 Oct 1973 327.02
## 179 Nov 1973 327.99
## 180 Dec 1973 328.48
## 181 Jan 1974 329.18
## 182 Feb 1974 330.55
## 183 Mar 1974 331.32
## 184 Apr 1974 332.48
## 185 May 1974 332.92
## 186 Jun 1974 332.08
## 187 Jul 1974 331.01
## 188 Aug 1974 329.23
## 189 Sep 1974 327.27
## 190 Oct 1974 327.21
## 191 Nov 1974 328.29
## 192 Dec 1974 329.41
## 193 Jan 1975 330.23
## 194 Feb 1975 331.25
## 195 Mar 1975 331.87
## 196 Apr 1975 333.14
## 197 May 1975 333.80
## 198 Jun 1975 333.43
## 199 Jul 1975 331.73
## 200 Aug 1975 329.90
## 201 Sep 1975 328.40
## 202 Oct 1975 328.17
## 203 Nov 1975 329.32
## 204 Dec 1975 330.59
## 205 Jan 1976 331.58
## 206 Feb 1976 332.39
## 207 Mar 1976 333.33
## 208 Apr 1976 334.41
## 209 May 1976 334.71
## 210 Jun 1976 334.17
## 211 Jul 1976 332.89
## 212 Aug 1976 330.77
## 213 Sep 1976 329.14
## 214 Oct 1976 328.78
## 215 Nov 1976 330.14
## 216 Dec 1976 331.52
## 217 Jan 1977 332.75
## 218 Feb 1977 333.24
## 219 Mar 1977 334.53
## 220 Apr 1977 335.90
## 221 May 1977 336.57
## 222 Jun 1977 336.10
## 223 Jul 1977 334.76
## 224 Aug 1977 332.59
## 225 Sep 1977 331.42
## 226 Oct 1977 330.98
## 227 Nov 1977 332.24
## 228 Dec 1977 333.68
## 229 Jan 1978 334.80
## 230 Feb 1978 335.22
## 231 Mar 1978 336.47
## 232 Apr 1978 337.59
## 233 May 1978 337.84
## 234 Jun 1978 337.72
## 235 Jul 1978 336.37
## 236 Aug 1978 334.51
## 237 Sep 1978 332.60
## 238 Oct 1978 332.38
## 239 Nov 1978 333.75
## 240 Dec 1978 334.78
## 241 Jan 1979 336.05
## 242 Feb 1979 336.59
## 243 Mar 1979 337.79
## 244 Apr 1979 338.71
## 245 May 1979 339.30
## 246 Jun 1979 339.12
## 247 Jul 1979 337.56
## 248 Aug 1979 335.92
## 249 Sep 1979 333.75
## 250 Oct 1979 333.70
## 251 Nov 1979 335.12
## 252 Dec 1979 336.56
## 253 Jan 1980 337.84
## 254 Feb 1980 338.19
## 255 Mar 1980 339.91
## 256 Apr 1980 340.60
## 257 May 1980 341.29
## 258 Jun 1980 341.00
## 259 Jul 1980 339.39
## 260 Aug 1980 337.43
## 261 Sep 1980 335.72
## 262 Oct 1980 335.84
## 263 Nov 1980 336.93
## 264 Dec 1980 338.04
## 265 Jan 1981 339.06
## 266 Feb 1981 340.30
## 267 Mar 1981 341.21
## 268 Apr 1981 342.33
## 269 May 1981 342.74
## 270 Jun 1981 342.08
## 271 Jul 1981 340.32
## 272 Aug 1981 338.26
## 273 Sep 1981 336.52
## 274 Oct 1981 336.68
## 275 Nov 1981 338.19
## 276 Dec 1981 339.44
## 277 Jan 1982 340.57
## 278 Feb 1982 341.44
## 279 Mar 1982 342.53
## 280 Apr 1982 343.39
## 281 May 1982 343.96
## 282 Jun 1982 343.18
## 283 Jul 1982 341.88
## 284 Aug 1982 339.65
## 285 Sep 1982 337.81
## 286 Oct 1982 337.69
## 287 Nov 1982 339.09
## 288 Dec 1982 340.32
## 289 Jan 1983 341.20
## 290 Feb 1983 342.35
## 291 Mar 1983 342.93
## 292 Apr 1983 344.77
## 293 May 1983 345.58
## 294 Jun 1983 345.14
## 295 Jul 1983 343.81
## 296 Aug 1983 342.21
## 297 Sep 1983 339.69
## 298 Oct 1983 339.82
## 299 Nov 1983 340.98
## 300 Dec 1983 342.82
## 301 Jan 1984 343.52
## 302 Feb 1984 344.33
## 303 Mar 1984 345.11
## 304 Apr 1984 346.88
## 305 May 1984 347.25
## 306 Jun 1984 346.62
## 307 Jul 1984 345.22
## 308 Aug 1984 343.11
## 309 Sep 1984 340.90
## 310 Oct 1984 341.18
## 311 Nov 1984 342.80
## 312 Dec 1984 344.04
## 313 Jan 1985 344.79
## 314 Feb 1985 345.82
## 315 Mar 1985 347.25
## 316 Apr 1985 348.17
## 317 May 1985 348.74
## 318 Jun 1985 348.07
## 319 Jul 1985 346.38
## 320 Aug 1985 344.51
## 321 Sep 1985 342.92
## 322 Oct 1985 342.62
## 323 Nov 1985 344.06
## 324 Dec 1985 345.38
## 325 Jan 1986 346.11
## 326 Feb 1986 346.78
## 327 Mar 1986 347.68
## 328 Apr 1986 349.37
## 329 May 1986 350.03
## 330 Jun 1986 349.37
## 331 Jul 1986 347.76
## 332 Aug 1986 345.73
## 333 Sep 1986 344.68
## 334 Oct 1986 343.99
## 335 Nov 1986 345.48
## 336 Dec 1986 346.72
## 337 Jan 1987 347.84
## 338 Feb 1987 348.29
## 339 Mar 1987 349.23
## 340 Apr 1987 350.80
## 341 May 1987 351.66
## 342 Jun 1987 351.07
## 343 Jul 1987 349.33
## 344 Aug 1987 347.92
## 345 Sep 1987 346.27
## 346 Oct 1987 346.18
## 347 Nov 1987 347.64
## 348 Dec 1987 348.78
## 349 Jan 1988 350.25
## 350 Feb 1988 351.54
## 351 Mar 1988 352.05
## 352 Apr 1988 353.41
## 353 May 1988 354.04
## 354 Jun 1988 353.62
## 355 Jul 1988 352.22
## 356 Aug 1988 350.27
## 357 Sep 1988 348.55
## 358 Oct 1988 348.72
## 359 Nov 1988 349.91
## 360 Dec 1988 351.18
## 361 Jan 1989 352.60
## 362 Feb 1989 352.92
## 363 Mar 1989 353.53
## 364 Apr 1989 355.26
## 365 May 1989 355.52
## 366 Jun 1989 354.97
## 367 Jul 1989 353.75
## 368 Aug 1989 351.52
## 369 Sep 1989 349.64
## 370 Oct 1989 349.83
## 371 Nov 1989 351.14
## 372 Dec 1989 352.37
## 373 Jan 1990 353.50
## 374 Feb 1990 354.55
## 375 Mar 1990 355.23
## 376 Apr 1990 356.04
## 377 May 1990 357.00
## 378 Jun 1990 356.07
## 379 Jul 1990 354.67
## 380 Aug 1990 352.76
## 381 Sep 1990 350.82
## 382 Oct 1990 351.04
## 383 Nov 1990 352.69
## 384 Dec 1990 354.07
## 385 Jan 1991 354.59
## 386 Feb 1991 355.63
## 387 Mar 1991 357.03
## 388 Apr 1991 358.48
## 389 May 1991 359.22
## 390 Jun 1991 358.12
## 391 Jul 1991 356.06
## 392 Aug 1991 353.92
## 393 Sep 1991 352.05
## 394 Oct 1991 352.11
## 395 Nov 1991 353.64
## 396 Dec 1991 354.89
## 397 Jan 1992 355.88
## 398 Feb 1992 356.63
## 399 Mar 1992 357.72
## 400 Apr 1992 359.07
## 401 May 1992 359.58
## 402 Jun 1992 359.17
## 403 Jul 1992 356.94
## 404 Aug 1992 354.92
## 405 Sep 1992 352.94
## 406 Oct 1992 353.23
## 407 Nov 1992 354.09
## 408 Dec 1992 355.33
## 409 Jan 1993 356.63
## 410 Feb 1993 357.10
## 411 Mar 1993 358.32
## 412 Apr 1993 359.41
## 413 May 1993 360.23
## 414 Jun 1993 359.55
## 415 Jul 1993 357.53
## 416 Aug 1993 355.48
## 417 Sep 1993 353.67
## 418 Oct 1993 353.95
## 419 Nov 1993 355.30
## 420 Dec 1993 356.78
## 421 Jan 1994 358.34
## 422 Feb 1994 358.89
## 423 Mar 1994 359.95
## 424 Apr 1994 361.25
## 425 May 1994 361.67
## 426 Jun 1994 360.94
## 427 Jul 1994 359.55
## 428 Aug 1994 357.49
## 429 Sep 1994 355.84
## 430 Oct 1994 356.00
## 431 Nov 1994 357.59
## 432 Dec 1994 359.05
## 433 Jan 1995 359.98
## 434 Feb 1995 361.03
## 435 Mar 1995 361.66
## 436 Apr 1995 363.48
## 437 May 1995 363.82
## 438 Jun 1995 363.30
## 439 Jul 1995 361.94
## 440 Aug 1995 359.50
## 441 Sep 1995 358.11
## 442 Oct 1995 357.80
## 443 Nov 1995 359.61
## 444 Dec 1995 360.74
## 445 Jan 1996 362.09
## 446 Feb 1996 363.29
## 447 Mar 1996 364.06
## 448 Apr 1996 364.76
## 449 May 1996 365.45
## 450 Jun 1996 365.01
## 451 Jul 1996 363.70
## 452 Aug 1996 361.54
## 453 Sep 1996 359.51
## 454 Oct 1996 359.65
## 455 Nov 1996 360.80
## 456 Dec 1996 362.38
## 457 Jan 1997 363.23
## 458 Feb 1997 364.06
## 459 Mar 1997 364.61
## 460 Apr 1997 366.40
## 461 May 1997 366.84
## 462 Jun 1997 365.68
## 463 Jul 1997 364.52
## 464 Aug 1997 362.57
## 465 Sep 1997 360.24
## 466 Oct 1997 360.83
## 467 Nov 1997 362.49
## 468 Dec 1997 364.34

The usage of r code “co2” is where the data of 468 observations of the amount of CO2 concentration released is stored.

2.3 Predicting the values

We want to know the predictions of the amount of CO2 concentration is released into the atmosphere in 1998 and 1999. So, we would use Prophet’s forecasting system to find the prediction.

model = prophet::prophet(dataFrame)

## Disabling weekly seasonality. Run prophet with weekly.seasonality=TRUE to override this.

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future = prophet::make_future_dataframe(model, periods=24, freq="month")#It creates future dates of 1998 and 1999 monthly.
forecast = predict(model, future)#It adds 24 future values into the data frame.
forecast[c('ds', 'yhat', 'yhat_lower', 'yhat_upper')]# Only showing the dates and predicted values

##             ds     yhat yhat_lower yhat_upper
## 1   1959-01-01 315.2762   314.7931   315.7300
## 2   1959-02-01 316.0336   315.5553   316.5073
## 3   1959-03-01 316.7481   316.2856   317.2136
## 4   1959-04-01 318.0609   317.5623   318.4996
## 5   1959-05-01 318.7030   318.2545   319.1704
## 6   1959-06-01 318.1193   317.6407   318.6029
## 7   1959-07-01 316.6084   316.1213   317.0696
## 8   1959-08-01 314.6953   314.2450   315.1563
## 9   1959-09-01 312.9642   312.4930   313.4151
## 10  1959-10-01 312.7374   312.2771   313.1748
## 11  1959-11-01 314.0959   313.5901   314.5548
## 12  1959-12-01 315.2924   314.8484   315.7557
## 13  1960-01-01 316.2917   315.8049   316.7616
## 14  1960-02-01 317.0542   316.5695   317.5195
## 15  1960-03-01 317.9654   317.4864   318.4542
## 16  1960-04-01 319.0991   318.6249   319.5850
## 17  1960-05-01 319.5777   319.1065   320.0200
## 18  1960-06-01 318.9925   318.5260   319.4490
## 19  1960-07-01 317.6160   317.1625   318.1198
## 20  1960-08-01 315.5506   315.0481   315.9606
## 21  1960-09-01 313.7822   313.3133   314.2542
## 22  1960-10-01 313.7908   313.3168   314.2602
## 23  1960-11-01 314.9618   314.4835   315.4359
## 24  1960-12-01 316.1571   315.6716   316.6366
## 25  1961-01-01 317.0873   316.6279   317.5499
## 26  1961-02-01 317.8129   317.3237   318.2199
## 27  1961-03-01 318.6954   318.2197   319.1720
## 28  1961-04-01 319.8688   319.3967   320.3552
## 29  1961-05-01 320.3969   319.9119   320.8697
## 30  1961-06-01 319.8073   319.3511   320.2444
## 31  1961-07-01 318.3795   317.9057   318.8389
## 32  1961-08-01 316.3578   315.8915   316.8170
## 33  1961-09-01 314.5966   314.1206   315.0909
## 34  1961-10-01 314.5201   314.0365   314.9685
## 35  1961-11-01 315.7468   315.2617   316.2112
## 36  1961-12-01 316.9370   316.4699   317.4147
## 37  1962-01-01 317.8843   317.4334   318.3524
## 38  1962-02-01 318.6170   318.1629   319.0522
## 39  1962-03-01 319.4066   318.9470   319.8801
## 40  1962-04-01 320.6397   320.1646   321.1029
## 41  1962-05-01 321.2163   320.7392   321.7086
## 42  1962-06-01 320.6210   320.1701   321.0395
## 43  1962-07-01 319.1424   318.7012   319.6161
## 44  1962-08-01 317.1653   316.6752   317.6393
## 45  1962-09-01 315.4103   314.9541   315.8919
## 46  1962-10-01 315.2493   314.7751   315.7430
## 47  1962-11-01 316.5069   316.0099   316.9576
## 48  1962-12-01 317.6670   317.2102   318.1133
## 49  1963-01-01 318.6058   318.1414   319.0610
## 50  1963-02-01 319.3192   318.8485   319.7643
## 51  1963-03-01 319.9940   319.5138   320.4775
## 52  1963-04-01 321.2628   320.7985   321.7567
## 53  1963-05-01 321.8624   321.3799   322.3302
## 54  1963-06-01 321.2347   320.7434   321.6862
## 55  1963-07-01 319.6813   319.1929   320.1460
## 56  1963-08-01 317.7242   317.2795   318.2224
## 57  1963-09-01 315.9491   315.4789   316.4476
## 58  1963-10-01 315.6797   315.1549   316.1589
## 59  1963-11-01 316.9943   316.5339   317.4653
## 60  1963-12-01 318.1482   317.6959   318.6197
## 61  1964-01-01 319.1035   318.6452   319.5853
## 62  1964-02-01 319.8211   319.3507   320.3190
## 63  1964-03-01 320.6903   320.2045   321.1421
## 64  1964-04-01 321.7791   321.2621   322.2387
## 65  1964-05-01 322.2322   321.7208   322.6936
## 66  1964-06-01 321.6207   321.1608   322.1007
## 67  1964-07-01 320.2187   319.7269   320.6863
## 68  1964-08-01 318.1269   317.6593   318.5877
## 69  1964-09-01 316.3323   315.8681   316.7961
## 70  1964-10-01 316.3154   315.8416   316.7712
## 71  1964-11-01 317.4600   316.9848   317.8845
## 72  1964-12-01 318.6299   318.1750   319.0904
## 73  1965-01-01 319.5337   319.1122   319.9947
## 74  1965-02-01 320.2329   319.7560   320.7175
## 75  1965-03-01 321.0917   320.6276   321.5588
## 76  1965-04-01 322.2387   321.7649   322.6854
## 77  1965-05-01 322.8013   322.3442   323.2497
## 78  1965-06-01 322.2472   321.8018   322.7391
## 79  1965-07-01 320.8538   320.3913   321.3490
## 80  1965-08-01 318.8678   318.4054   319.3156
## 81  1965-09-01 317.1421   316.6610   317.6222
## 82  1965-10-01 317.1001   316.6231   317.5875
## 83  1965-11-01 318.3624   317.8939   318.8736
## 84  1965-12-01 319.5870   319.0916   320.0492
## 85  1966-01-01 320.5699   320.1064   321.0413
## 86  1966-02-01 321.3383   320.8474   321.8128
## 87  1966-03-01 322.1601   321.6980   322.6254
## 88  1966-04-01 323.4287   322.9612   323.8897
## 89  1966-05-01 324.0398   323.5841   324.5160
## 90  1966-06-01 323.4801   323.0296   323.9559
## 91  1966-07-01 322.0359   321.5628   322.4933
## 92  1966-08-01 320.0561   319.5689   320.5042
## 93  1966-09-01 318.2984   317.8364   318.7810
## 94  1966-10-01 318.1348   317.6727   318.6274
## 95  1966-11-01 319.4151   318.9417   319.9033
## 96  1966-12-01 320.5971   320.0963   321.0449
## 97  1967-01-01 321.5585   321.0832   322.0449
## 98  1967-02-01 322.2947   321.8342   322.7642
## 99  1967-03-01 322.9900   322.5051   323.4369
## 100 1967-04-01 324.2815   323.8087   324.7588
## 101 1967-05-01 324.9030   324.4174   325.3868
## 102 1967-06-01 324.2980   323.8061   324.7621
## 103 1967-07-01 322.7665   322.2749   323.2279
## 104 1967-08-01 320.8321   320.3399   321.3342
## 105 1967-09-01 319.0797   318.5960   319.5434
## 106 1967-10-01 318.8706   318.4177   319.3559
## 107 1967-11-01 320.2474   319.8157   320.7155
## 108 1967-12-01 321.4616   321.0034   321.9788
## 109 1968-01-01 322.4792   322.0078   322.9553
## 110 1968-02-01 323.2600   322.7879   323.7515
## 111 1968-03-01 324.1883   323.7106   324.6138
## 112 1968-04-01 325.3403   324.8271   325.7984
## 113 1968-05-01 325.8546   325.4217   326.3306
## 114 1968-06-01 325.3062   324.8244   325.7693
## 115 1968-07-01 323.9655   323.5042   324.4490
## 116 1968-08-01 321.9369   321.4430   322.4314
## 117 1968-09-01 320.2054   319.7439   320.6687
## 118 1968-10-01 320.2497   319.7608   320.7194
## 119 1968-11-01 321.4575   320.9735   321.9029
## 120 1968-12-01 322.6885   322.2397   323.1717
## 121 1969-01-01 323.6659   323.1944   324.1570
## 122 1969-02-01 324.4386   323.9982   324.8979
## 123 1969-03-01 325.3639   324.8684   325.8401
## 124 1969-04-01 326.5845   326.1134   327.0502
## 125 1969-05-01 327.1582   326.6727   327.6035
## 126 1969-06-01 326.6158   326.1531   327.0691
## 127 1969-07-01 325.2337   324.7562   325.7174
## 128 1969-08-01 323.2593   322.7791   323.7256
## 129 1969-09-01 321.5452   321.0782   322.0001
## 130 1969-10-01 321.5145   321.0510   321.9815
## 131 1969-11-01 322.7883   322.3253   323.2394
## 132 1969-12-01 324.0243   323.6054   324.4907
## 133 1970-01-01 325.0188   324.5381   325.4942
## 134 1970-02-01 325.7988   325.3524   326.2755
## 135 1970-03-01 326.6311   326.1869   327.0949
## 136 1970-04-01 327.8456   327.3789   328.2792
## 137 1970-05-01 328.4043   327.9507   328.8578
## 138 1970-06-01 327.7904   327.3092   328.2435
## 139 1970-07-01 326.2939   325.8221   326.7293
## 140 1970-08-01 324.2983   323.8444   324.7745
## 141 1970-09-01 322.5247   322.0371   322.9832
## 142 1970-10-01 322.3459   321.9016   322.8561
## 143 1970-11-01 323.6103   323.1217   324.0785
## 144 1970-12-01 324.7771   324.3240   325.2570
## 145 1971-01-01 325.7227   325.2279   326.1679
## 146 1971-02-01 326.4430   325.9695   326.9152
## 147 1971-03-01 327.1241   326.6236   327.5810
## 148 1971-04-01 328.3998   327.9486   328.8525
## 149 1971-05-01 329.0060   328.5285   329.4723
## 150 1971-06-01 328.3852   327.8961   328.8881
## 151 1971-07-01 326.9109   326.4266   327.4151
## 152 1971-08-01 325.0357   324.5362   325.5006
## 153 1971-09-01 323.3425   322.8450   323.8041
## 154 1971-10-01 323.1523   322.7063   323.6106
## 155 1971-11-01 324.5487   324.0974   325.0151
## 156 1971-12-01 325.7819   325.3195   326.2647
## 157 1972-01-01 326.8191   326.3638   327.3025
## 158 1972-02-01 327.6194   327.2003   328.0787
## 159 1972-03-01 328.5661   328.0860   329.0401
## 160 1972-04-01 329.7377   329.2945   330.2012
## 161 1972-05-01 330.2709   329.7962   330.7158
## 162 1972-06-01 329.7422   329.2536   330.2115
## 163 1972-07-01 328.4203   327.9504   328.9053
## 164 1972-08-01 326.4113   325.9467   326.8941
## 165 1972-09-01 324.6994   324.2176   325.1844
## 166 1972-10-01 324.7858   324.2798   325.2373
## 167 1972-11-01 326.0372   325.5695   326.5000
## 168 1972-12-01 327.3103   326.8328   327.7770
## 169 1973-01-01 328.3208   327.8616   328.7963
## 170 1973-02-01 329.1268   328.6680   329.5581
## 171 1973-03-01 330.0819   329.6110   330.5572
## 172 1973-04-01 331.3357   330.8530   331.7795
## 173 1973-05-01 331.9416   331.4837   332.3970
## 174 1973-06-01 331.4323   330.9910   331.9168
## 175 1973-07-01 330.0823   329.5785   330.5397
## 176 1973-08-01 328.1410   327.6810   328.5921
## 177 1973-09-01 326.4601   326.0138   326.9129
## 178 1973-10-01 326.4615   326.0141   326.9530
## 179 1973-11-01 327.7685   327.2781   328.2364
## 180 1973-12-01 329.0365   328.5907   329.5104
## 181 1974-01-01 329.9638   329.5085   330.4326
## 182 1974-02-01 330.6764   330.2031   331.1712
## 183 1974-03-01 331.4479   330.9796   331.9381
## 184 1974-04-01 332.6610   332.2109   333.1500
## 185 1974-05-01 333.2181   332.7239   333.6968
## 186 1974-06-01 332.6027   332.1318   333.0483
## 187 1974-07-01 331.1047   330.6479   331.5677
## 188 1974-08-01 329.1075   328.6380   329.5583
## 189 1974-09-01 327.3324   326.8391   327.8024
## 190 1974-10-01 327.1521   326.6882   327.6377
## 191 1974-11-01 328.4150   327.9492   328.8633
## 192 1974-12-01 329.5802   329.1087   330.0571
## 193 1975-01-01 330.5243   330.0767   330.9732
## 194 1975-02-01 331.2430   330.7798   331.6990
## 195 1975-03-01 331.9227   331.4299   332.3676
## 196 1975-04-01 333.2346   332.7311   333.6790
## 197 1975-05-01 333.8758   333.3862   334.3607
## 198 1975-06-01 333.2912   332.8549   333.7705
## 199 1975-07-01 331.7795   331.3346   332.2159
## 200 1975-08-01 329.8655   329.4065   330.3171
## 201 1975-09-01 328.1335   327.6636   328.6382
## 202 1975-10-01 327.9058   327.4660   328.3710
## 203 1975-11-01 329.2634   328.7944   329.7040
## 204 1975-12-01 330.4591   330.0169   330.9545
## 205 1976-01-01 331.4575   330.9884   331.9305
## 206 1976-02-01 332.2191   331.7456   332.6734
## 207 1976-03-01 333.1295   332.7004   333.5663
## 208 1976-04-01 334.2623   333.8055   334.7315
## 209 1976-05-01 334.7580   334.3101   335.2256
## 210 1976-06-01 334.1904   333.6967   334.6181
## 211 1976-07-01 332.8900   332.4235   333.3451
## 212 1976-08-01 330.9031   330.4349   331.3857
## 213 1976-09-01 329.2134   328.7219   329.6780
## 214 1976-10-01 329.2980   328.8470   329.7685
## 215 1976-11-01 330.5476   330.0780   331.0120
## 216 1976-12-01 331.8190   331.3513   332.2990
## 217 1977-01-01 332.8277   332.3658   333.3034
## 218 1977-02-01 333.6318   333.1855   334.1157
## 219 1977-03-01 334.5854   334.1180   335.0821
## 220 1977-04-01 335.8374   335.3802   336.2860
## 221 1977-05-01 336.4415   335.9568   336.9423
## 222 1977-06-01 335.9304   335.5079   336.3875
## 223 1977-07-01 334.5787   334.0932   335.0198
## 224 1977-08-01 332.6356   332.1501   333.1261
## 225 1977-09-01 330.9529   330.4893   331.3932
## 226 1977-10-01 330.9411   330.4507   331.4242
## 227 1977-11-01 332.2346   331.7691   332.6948
## 228 1977-12-01 333.4894   333.0092   333.9684
## 229 1978-01-01 334.5035   334.0349   334.9868
## 230 1978-02-01 335.3031   334.8153   335.7343
## 231 1978-03-01 336.1530   335.7089   336.6278
## 232 1978-04-01 337.4529   336.9967   337.9179
## 233 1978-05-01 338.0941   337.6584   338.5447
## 234 1978-06-01 337.5656   337.0768   338.0211
## 235 1978-07-01 336.1516   335.7059   336.6133
## 236 1978-08-01 334.2414   333.7196   334.7002
## 237 1978-09-01 332.5531   332.0947   333.0564
## 238 1978-10-01 332.4568   331.9785   332.9562
## 239 1978-11-01 333.8066   333.3265   334.2675
## 240 1978-12-01 335.0559   334.5961   335.5501
## 241 1979-01-01 336.0874   335.5848   336.5688
## 242 1979-02-01 336.8936   336.4323   337.3641
## 243 1979-03-01 337.6522   337.1902   338.1042
## 244 1979-04-01 339.0138   338.5274   339.4735
## 245 1979-05-01 339.7031   339.2176   340.1945
## 246 1979-06-01 339.1682   338.7086   339.6380
## 247 1979-07-01 337.7046   337.2592   338.1887
## 248 1979-08-01 335.8402   335.3448   336.3096
## 249 1979-09-01 334.1579   333.6807   334.6262
## 250 1979-10-01 333.9783   333.4964   334.4610
## 251 1979-11-01 335.3856   334.9314   335.8648
## 252 1979-12-01 336.6293   336.1997   337.1026
## 253 1980-01-01 337.6774   337.2048   338.1622
## 254 1980-02-01 338.4887   338.0371   338.9719
## 255 1980-03-01 339.4456   338.9676   339.8836
## 256 1980-04-01 340.6169   340.1454   341.0954
## 257 1980-05-01 341.1499   340.6858   341.6152
## 258 1980-06-01 340.6209   340.1610   341.0901
## 259 1980-07-01 339.2988   338.8694   339.7776
## 260 1980-08-01 337.2896   336.8099   337.7455
## 261 1980-09-01 335.5775   335.1331   336.0156
## 262 1980-10-01 335.6405   335.1970   336.0833
## 263 1980-11-01 336.8677   336.4032   337.3274
## 264 1980-12-01 338.1174   337.6525   338.5697
## 265 1981-01-01 339.1038   338.6416   339.5656
## 266 1981-02-01 339.8855   339.4406   340.3458
## 267 1981-03-01 340.8189   340.3724   341.2497
## 268 1981-04-01 342.0485   341.6119   342.5307
## 269 1981-05-01 342.6310   342.1805   343.0687
## 270 1981-06-01 342.0976   341.6212   342.5493
## 271 1981-07-01 340.6962   340.2335   341.1496
## 272 1981-08-01 338.7020   338.2403   339.1820
## 273 1981-09-01 336.9681   336.4781   337.4493
## 274 1981-10-01 336.9181   336.4594   337.4289
## 275 1981-11-01 338.1722   337.7114   338.6607
## 276 1981-12-01 339.3889   338.9172   339.8387
## 277 1982-01-01 340.3636   339.8830   340.8081
## 278 1982-02-01 341.1237   340.6363   341.6046
## 279 1982-03-01 341.9380   341.4995   342.3960
## 280 1982-04-01 343.1985   342.7460   343.6779
## 281 1982-05-01 343.8016   343.3343   344.2800
## 282 1982-06-01 343.2337   342.7753   343.7098
## 283 1982-07-01 341.7815   341.3015   342.2488
## 284 1982-08-01 339.8319   339.3522   340.2846
## 285 1982-09-01 338.1580   337.6862   338.6169
## 286 1982-10-01 338.0756   337.5699   338.5544
## 287 1982-11-01 339.4397   338.9491   339.9018
## 288 1982-12-01 340.7029   340.2502   341.2162
## 289 1983-01-01 341.7482   341.3086   342.2135
## 290 1983-02-01 342.5682   342.1134   343.0416
## 291 1983-03-01 343.3393   342.8511   343.7904
## 292 1983-04-01 344.7147   344.2429   345.1806
## 293 1983-05-01 345.4173   344.9448   345.8782
## 294 1983-06-01 344.8962   344.4172   345.3523
## 295 1983-07-01 343.4459   342.9756   343.8972
## 296 1983-08-01 341.5954   341.1226   342.0304
## 297 1983-09-01 339.9268   339.4255   340.3774
## 298 1983-10-01 339.7606   339.2842   340.2169
## 299 1983-11-01 341.1817   340.7091   341.6779
## 300 1983-12-01 342.4258   341.9559   342.8724
## 301 1984-01-01 343.4743   342.9856   343.9404
## 302 1984-02-01 344.2860   343.7940   344.7188
## 303 1984-03-01 345.2433   344.7966   345.7290
## 304 1984-04-01 346.4263   345.9264   346.9064
## 305 1984-05-01 346.9705   346.4917   347.4164
## 306 1984-06-01 346.4531   345.9661   346.9244
## 307 1984-07-01 345.1422   344.6495   345.5824
## 308 1984-08-01 343.1445   342.6880   343.5960
## 309 1984-09-01 341.4440   341.0197   341.8788
## 310 1984-10-01 341.5182   341.0376   341.9557
## 311 1984-11-01 342.7570   342.3277   343.2590
## 312 1984-12-01 344.0179   343.5556   344.5236
## 313 1985-01-01 345.0159   344.5430   345.4882
## 314 1985-02-01 345.8092   345.3551   346.2803
## 315 1985-03-01 346.7238   346.2675   347.1710
## 316 1985-04-01 347.9325   347.4762   348.3572
## 317 1985-05-01 348.4948   348.0003   348.9359
## 318 1985-06-01 347.9406   347.4657   348.3933
## 319 1985-07-01 346.5470   346.0804   347.0163
## 320 1985-08-01 344.5608   344.1114   345.0303
## 321 1985-09-01 342.8349   342.3695   343.2833
## 322 1985-10-01 342.7927   342.3209   343.2594
## 323 1985-11-01 344.0547   343.6284   344.5321
## 324 1985-12-01 345.2792   344.8101   345.7571
## 325 1986-01-01 346.2619   345.8035   346.7127
## 326 1986-02-01 347.0300   346.5483   347.5161
## 327 1986-03-01 347.8516   347.3421   348.3018
## 328 1986-04-01 349.1201   348.6363   349.5890
## 329 1986-05-01 349.7310   349.2672   350.2768
## 330 1986-06-01 349.2299   348.7797   349.7025
## 331 1986-07-01 347.8425   347.3610   348.3259
## 332 1986-08-01 345.9597   345.4701   346.4396
## 333 1986-09-01 344.2989   343.8457   344.7365
## 334 1986-10-01 344.2292   343.7713   344.7162
## 335 1986-11-01 345.6064   345.1009   346.1062
## 336 1986-12-01 346.8823   346.4128   347.3224
## 337 1987-01-01 347.9407   347.4680   348.3978
## 338 1987-02-01 348.7738   348.3027   349.2318
## 339 1987-03-01 349.5567   349.0963   350.0196
## 340 1987-04-01 350.9451   350.5164   351.4315
## 341 1987-05-01 351.6605   351.1673   352.1225
## 342 1987-06-01 351.1525   350.6808   351.6216
## 343 1987-07-01 349.7148   349.2259   350.1649
## 344 1987-08-01 347.8774   347.3803   348.3272
## 345 1987-09-01 346.2679   345.7877   346.7526
## 346 1987-10-01 346.1588   345.6908   346.6282
## 347 1987-11-01 347.6389   347.1798   348.1057
## 348 1987-12-01 348.9532   348.4803   349.4257
## 349 1988-01-01 350.0740   349.5955   350.4870
## 350 1988-02-01 350.9582   350.4712   351.4109
## 351 1988-03-01 351.9832   351.5161   352.4528
## 352 1988-04-01 353.2385   352.7454   353.6945
## 353 1988-05-01 353.8528   353.3854   354.3374
## 354 1988-06-01 353.4078   352.9474   353.8665
## 355 1988-07-01 352.1670   351.7031   352.6241
## 356 1988-08-01 350.2417   349.7843   350.7042
## 357 1988-09-01 348.6136   348.1128   349.0705
## 358 1988-10-01 348.7579   348.2807   349.2154
## 359 1988-11-01 350.0690   349.6065   350.5217
## 360 1988-12-01 351.2675   350.8123   351.7543
## 361 1989-01-01 352.2010   351.7384   352.6979
## 362 1989-02-01 352.9298   352.5081   353.4356
## 363 1989-03-01 353.8153   353.3409   354.2562
## 364 1989-04-01 354.9920   354.5572   355.4655
## 365 1989-05-01 355.5232   355.0596   355.9741
## 366 1989-06-01 354.9369   354.4740   355.3851
## 367 1989-07-01 353.5123   353.0661   353.9733
## 368 1989-08-01 351.4939   350.9946   351.9795
## 369 1989-09-01 349.7359   349.2611   350.2403
## 370 1989-10-01 349.6627   349.2094   350.1545
## 371 1989-11-01 350.8926   350.4481   351.3655
## 372 1989-12-01 352.0860   351.5914   352.5631
## 373 1990-01-01 353.0366   352.5617   353.5241
## 374 1990-02-01 353.7726   353.3176   354.2080
## 375 1990-03-01 354.6108   354.1467   355.0805
## 376 1990-04-01 355.8976   355.4292   356.3439
## 377 1990-05-01 356.5262   356.0450   357.0455
## 378 1990-06-01 355.9846   355.5146   356.5042
## 379 1990-07-01 354.5579   354.0915   354.9874
## 380 1990-08-01 352.6346   352.1753   353.1071
## 381 1990-09-01 350.9332   350.4347   351.3678
## 382 1990-10-01 350.8243   350.3392   351.3045
## 383 1990-11-01 352.1610   351.7087   352.6169
## 384 1990-12-01 353.3976   352.9301   353.8769
## 385 1991-01-01 354.4155   353.9789   354.8589
## 386 1991-02-01 355.2080   354.7207   355.6946
## 387 1991-03-01 355.9543   355.5046   356.4339
## 388 1991-04-01 357.3022   356.8536   357.7454
## 389 1991-05-01 357.9783   357.5191   358.4545
## 390 1991-06-01 357.4298   356.9592   357.8907
## 391 1991-07-01 355.9529   355.4731   356.4005
## 392 1991-08-01 354.0749   353.6362   354.5583
## 393 1991-09-01 352.3789   351.8929   352.8911
## 394 1991-10-01 352.1861   351.7387   352.6737
## 395 1991-11-01 353.5798   353.1266   354.0558
## 396 1991-12-01 354.8103   354.3782   355.2868
## 397 1992-01-01 355.8447   355.3723   356.2941
## 398 1992-02-01 356.6423   356.1539   357.1034
## 399 1992-03-01 357.5864   357.1295   358.0257
## 400 1992-04-01 358.7552   358.2841   359.2218
## 401 1992-05-01 359.2858   358.8399   359.7553
## 402 1992-06-01 358.7543   358.2935   359.2124
## 403 1992-07-01 357.4298   356.9585   357.9167
## 404 1992-08-01 355.4180   354.9875   355.8746
## 405 1992-09-01 353.7033   353.2635   354.1880
## 406 1992-10-01 353.7639   353.2966   354.2245
## 407 1992-11-01 354.9886   354.5199   355.4884
## 408 1992-12-01 356.2359   355.7581   356.6968
## 409 1993-01-01 357.2197   356.7728   357.7051
## 410 1993-02-01 357.9990   357.5141   358.4290
## 411 1993-03-01 358.9301   358.4615   359.3880
## 412 1993-04-01 360.1572   359.7101   360.6039
## 413 1993-05-01 360.7372   360.2834   361.2088
## 414 1993-06-01 360.2013   359.7433   360.6574
## 415 1993-07-01 358.8254   358.3484   359.2818
## 416 1993-08-01 356.8575   356.3908   357.3322
## 417 1993-09-01 355.1499   354.6600   355.6117
## 418 1993-10-01 355.1255   354.6702   355.6082
## 419 1993-11-01 356.4058   355.9080   356.8539
## 420 1993-12-01 357.6480   357.1883   358.1070
## 421 1994-01-01 358.6490   358.1887   359.1401
## 422 1994-02-01 359.4355   358.9876   359.9036
## 423 1994-03-01 360.2736   359.7972   360.7513
## 424 1994-04-01 361.5604   361.0802   362.0227
## 425 1994-05-01 362.1890   361.7099   362.6432
## 426 1994-06-01 361.6474   361.1585   362.1190
## 427 1994-07-01 360.2208   359.7665   360.6834
## 428 1994-08-01 358.2974   357.8305   358.7838
## 429 1994-09-01 356.5961   356.1533   357.0430
## 430 1994-10-01 356.4871   356.0383   356.9518
## 431 1994-11-01 357.8238   357.3665   358.2878
## 432 1994-12-01 359.0604   358.5720   359.5356
## 433 1995-01-01 360.0783   359.5738   360.5455
## 434 1995-02-01 360.8709   360.3870   361.3140
## 435 1995-03-01 361.6172   361.1193   362.0980
## 436 1995-04-01 362.9651   362.4718   363.4199
## 437 1995-05-01 363.6412   363.1522   364.1014
## 438 1995-06-01 363.0926   362.6283   363.5266
## 439 1995-07-01 361.6157   361.1440   362.0928
## 440 1995-08-01 359.7378   359.2994   360.2100
## 441 1995-09-01 358.0418   357.5914   358.4882
## 442 1995-10-01 357.8489   357.3669   358.2805
## 443 1995-11-01 359.2426   358.7726   359.6977
## 444 1995-12-01 360.4731   359.9710   360.9456
## 445 1996-01-01 361.5075   361.0087   361.9567
## 446 1996-02-01 362.3051   361.7894   362.7768
## 447 1996-03-01 363.2492   362.7551   363.7300
## 448 1996-04-01 364.4181   363.9526   364.8918
## 449 1996-05-01 364.9486   364.4660   365.4248
## 450 1996-06-01 364.4171   363.9589   364.8904
## 451 1996-07-01 363.0926   362.6518   363.5808
## 452 1996-08-01 361.0808   360.5913   361.5475
## 453 1996-09-01 359.3662   358.8589   359.8449
## 454 1996-10-01 359.4268   358.9589   359.8655
## 455 1996-11-01 360.6515   360.1682   361.1343
## 456 1996-12-01 361.8987   361.4409   362.3547
## 457 1997-01-01 362.8826   362.4361   363.3422
## 458 1997-02-01 363.6619   363.2218   364.1467
## 459 1997-03-01 364.5929   364.1470   365.0357
## 460 1997-04-01 365.8200   365.3593   366.3030
## 461 1997-05-01 366.4001   365.9589   366.8880
## 462 1997-06-01 365.8641   365.3594   366.3802
## 463 1997-07-01 364.4883   364.0445   364.9609
## 464 1997-08-01 362.5203   362.0713   363.0052
## 465 1997-09-01 360.8128   360.3441   361.3097
## 466 1997-10-01 360.7883   360.3112   361.2482
## 467 1997-11-01 362.0687   361.6181   362.5326
## 468 1997-12-01 363.3109   362.8506   363.7938
## 469 1998-01-01 364.3119   363.8362   364.7818
## 470 1998-02-01 365.0984   364.6153   365.5495
## 471 1998-03-01 365.9365   365.4385   366.3823
## 472 1998-04-01 367.2233   366.7660   367.7111
## 473 1998-05-01 367.8519   367.3668   368.3347
## 474 1998-06-01 367.3103   366.8307   367.7857
## 475 1998-07-01 365.8836   365.4126   366.4094
## 476 1998-08-01 363.9603   363.4629   364.4664
## 477 1998-09-01 362.2589   361.7850   362.8022
## 478 1998-10-01 362.1500   361.6137   362.6654
## 479 1998-11-01 363.4867   362.9459   364.0284
## 480 1998-12-01 364.7233   364.1482   365.2520
## 481 1999-01-01 365.7412   365.2213   366.3171
## 482 1999-02-01 366.5337   365.9647   367.1387
## 483 1999-03-01 367.2800   366.6498   367.8830
## 484 1999-04-01 368.6279   368.0343   369.3507
## 485 1999-05-01 369.3040   368.6255   370.0261
## 486 1999-06-01 368.7555   368.0493   369.4820
## 487 1999-07-01 367.2786   366.5287   368.0012
## 488 1999-08-01 365.4006   364.5994   366.1796
## 489 1999-09-01 363.7046   362.8564   364.5173
## 490 1999-10-01 363.5118   362.5964   364.3352
## 491 1999-11-01 364.9055   364.0359   365.8334
## 492 1999-12-01 366.1360   365.1653   367.1515

The code ‘make_future_dataframe’ is where future dates is created in number of periods you picked.

2.4 Plot

2.4.1 Display

plot(model,forecast, xlab="Years", ylab="Concentration of CO2 (ppm)",main="Mauna Loa Atmospheric CO2 Concentration")

prophet::prophet_plot_components(model, forecast)#Broke dowm into trend and yearly seasonality.

These graphs show the full observations including the future dates and its predicted values.We can tell that the amount of CO2 concentration released increases during the spring and summer, but decreases during autumn and winter, where the highest peak in the every year is May. This is due to the high temperatures during spring and summer where CO2 are released quickly. Low temperature, on the other hand, do slow down release of concentration. But as years goes by, the concentration of CO2 gradually increases. This is because of emissions caused by human, damaging the climate changes. One example for this is deforestation around Mauna Loa, where trees, which stores CO2, are cut down, releasing more CO2. concentrations.

2.4.2 Dygraph

library(dygraphs)

## Warning: package 'dygraphs' was built under R version 4.4.3

prediction<-forecast[c('ds', 'yhat', 'yhat_lower', 'yhat_upper')]#Predicted values
dygraph(prediction, main = "New Concentration") %>% dyRangeSelector(dateWindow = c("1998-01-01", "1999-12-01"))# Dygraph showing the predictions in 1998 and 1999 with upper bound and lower bound

The dygraph shows the predictions of the values of CO2 concentration being released to the atmosphere. We can tell that it follows the same pattern as the original observations.

2.5 Reference

https://scrippsco2.ucsd.edu/data/atmospheric_co2/.

3 Peyton Manning’s Wikipedia Page

Peyton Manning

3.1 Introduction

The forecasting system can also be use to show the time series of how many people have visited on one Wikipedia page and is capable of showing multiple seasonality and growth rates. A Wikipedia page of a former NFL player Peyton Manning is one of the example.He is one of NFL greatest quarterbacks of all time. He played for Indianapolis Colts for 14 seasons and Denver Broncos for 4 seasons before retiring in 2016. A time series showing the data of daily views of Peyton Manning is stored on this website: https://github.com/facebook/prophet/blob/main/examples/example_wp_log_peyton_manning.csv This time series shows 2905 observations taken from 10th December 2007 to 20 January 2016 daily. Because of high differences in number of views between one date and another date, it could lead to lots of anomalous values,log transformations was used in order to stabilise the variance. Therefore daily views were taken in log.

3.2 Data

This is the first 200 observations of daily views of Peyton Manning at Wikipedia.

dataFrame2 <- read.csv('https://raw.githubusercontent.com/facebook/prophet/main/examples/example_wp_log_peyton_manning.csv')#Creating this time series from the website into data frame.
dataFrame2

##              ds         y
## 1    2007-12-10  9.590761
## 2    2007-12-11  8.519590
## 3    2007-12-12  8.183677
## 4    2007-12-13  8.072467
## 5    2007-12-14  7.893572
## 6    2007-12-15  7.783641
## 7    2007-12-16  8.414052
## 8    2007-12-17  8.829226
## 9    2007-12-18  8.382518
## 10   2007-12-19  8.069655
## 11   2007-12-20  7.879291
## 12   2007-12-21  7.761745
## 13   2007-12-22  7.529406
## 14   2007-12-23  8.385261
## 15   2007-12-24  8.620111
## 16   2007-12-25  7.852439
## 17   2007-12-26  7.853993
## 18   2007-12-27  8.051978
## 19   2007-12-28  7.926603
## 20   2007-12-29  7.838343
## 21   2007-12-30  9.703145
## 22   2007-12-31  9.385973
## 23   2008-01-01  8.293800
## 24   2008-01-02  8.434681
## 25   2008-01-03  8.262043
## 26   2008-01-04  8.106816
## 27   2008-01-05  7.950150
## 28   2008-01-06  9.509259
## 29   2008-01-07  8.846785
## 30   2008-01-08  8.430545
## 31   2008-01-09  8.248267
## 32   2008-01-10  8.281724
## 33   2008-01-11  8.292799
## 34   2008-01-12  8.199189
## 35   2008-01-13  9.996522
## 36   2008-01-14 10.127071
## 37   2008-01-15  8.933796
## 38   2008-01-16  8.566174
## 39   2008-01-17  8.547722
## 40   2008-01-18  8.399760
## 41   2008-01-19  8.223091
## 42   2008-01-20  8.838987
## 43   2008-01-21 10.897202
## 44   2008-01-22  9.444938
## 45   2008-01-23  8.923325
## 46   2008-01-24  8.543446
## 47   2008-01-25  8.495561
## 48   2008-01-26  8.417373
## 49   2008-01-27  8.572628
## 50   2008-01-28  8.736489
## 51   2008-01-29  8.634087
## 52   2008-01-30  8.673513
## 53   2008-02-01  8.824237
## 54   2008-02-02  8.537976
## 55   2008-02-03  9.698061
## 56   2008-02-04 12.097457
## 57   2008-02-05 10.635278
## 58   2008-02-06  9.691717
## 59   2008-02-07  9.315601
## 60   2008-02-08  8.970813
## 61   2008-02-09  8.589142
## 62   2008-02-10  8.617400
## 63   2008-02-11  8.616314
## 64   2008-02-12  8.215547
## 65   2008-02-13  8.064951
## 66   2008-02-14  8.113427
## 67   2008-02-15  7.799343
## 68   2008-02-16  7.627544
## 69   2008-02-17  7.555905
## 70   2008-02-18  7.711549
## 71   2008-02-19  7.788626
## 72   2008-02-20  7.708411
## 73   2008-02-21  7.768533
## 74   2008-02-22  7.695303
## 75   2008-02-23  7.378384
## 76   2008-02-24  7.910591
## 77   2008-02-25  7.626570
## 78   2008-02-26  7.573531
## 79   2008-02-27  7.567863
## 80   2008-02-29  7.552237
## 81   2008-03-02  7.336937
## 82   2008-03-05  8.124743
## 83   2008-03-06  7.887584
## 84   2008-03-07  7.819636
## 85   2008-03-08  7.383989
## 86   2008-03-09  7.814400
## 87   2008-03-10  7.542213
## 88   2008-03-11  7.548556
## 89   2008-03-12  7.688913
## 90   2008-03-13  7.477038
## 91   2008-03-14  7.358831
## 92   2008-03-15  7.032624
## 93   2008-03-16  7.118016
## 94   2008-03-17  7.349874
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## 96   2008-03-19  7.363914
## 97   2008-03-20  7.277939
## 98   2008-03-21  7.251345
## 99   2008-03-22  7.002156
## 100  2008-03-23  7.163947
## 101  2008-03-24  7.759187
## 102  2008-03-25  7.518607
## 103  2008-03-26  7.413970
## 104  2008-03-27  7.442493
## 105  2008-03-28  7.228388
## 106  2008-03-29  6.991177
## 107  2008-03-30  7.211557
## 108  2008-03-31  7.311218
## 109  2008-04-01  7.349231
## 110  2008-04-02  7.514255
## 111  2008-04-03  7.393263
## 112  2008-04-04  7.286192
## 113  2008-04-05  7.273093
## 114  2008-04-06  7.168580
## 115  2008-04-07  7.611348
## 116  2008-04-08  7.617760
## 117  2008-04-09  7.425954
## 118  2008-04-10  8.182000
## 119  2008-04-11  7.399398
## 120  2008-04-12  7.106606
## 121  2008-04-13  7.080868
## 122  2008-04-14  7.421178
## 123  2008-04-15  7.491645
## 124  2008-04-16  7.385851
## 125  2008-04-17  7.682943
## 126  2008-04-18  7.688913
## 127  2008-04-19  7.259116
## 128  2008-04-20  8.144969
## 129  2008-04-21  8.713911
## 130  2008-04-22  8.091015
## 131  2008-04-23  7.840313
## 132  2008-04-24  7.648740
## 133  2008-04-25  8.020928
## 134  2008-04-26  7.830028
## 135  2008-04-27  7.727535
## 136  2008-04-28  7.835975
## 137  2008-04-29  7.626570
## 138  2008-04-30  7.644441
## 139  2008-05-01  7.548556
## 140  2008-05-02  7.440734
## 141  2008-05-03  7.073270
## 142  2008-05-04  7.026427
## 143  2008-05-05  7.392032
## 144  2008-05-06  7.293018
## 145  2008-05-07  7.361375
## 146  2008-05-08  7.512618
## 147  2008-05-09  7.460490
## 148  2008-05-10  7.114769
## 149  2008-05-11  7.125283
## 150  2008-05-12  7.455877
## 151  2008-05-13  7.317212
## 152  2008-05-14  7.410347
## 153  2008-05-15  7.402452
## 154  2008-05-16  7.294377
## 155  2008-05-17  6.989335
## 156  2008-05-18  6.993015
## 157  2008-05-19  7.431300
## 158  2008-05-20  7.362011
## 159  2008-05-21  7.454720
## 160  2008-05-22  7.368340
## 161  2008-05-23  7.143618
## 162  2008-05-24  6.835185
## 163  2008-05-25  6.890609
## 164  2008-05-26  6.974479
## 165  2008-05-27  7.266129
## 166  2008-05-28  7.270313
## 167  2008-05-29  7.265430
## 168  2008-05-30  7.157735
## 169  2008-05-31  6.865891
## 170  2008-06-03  7.153834
## 171  2008-06-04  7.216709
## 172  2008-06-05  7.201916
## 173  2008-06-06  7.212294
## 174  2008-06-07  7.186144
## 175  2008-06-08  6.820016
## 176  2008-06-09  6.882437
## 177  2008-06-10  7.183112
## 178  2008-06-11  7.242798
## 179  2008-06-12  7.192934
## 180  2008-06-13  7.183871
## 181  2008-06-14  6.970730
## 182  2008-06-15  6.917706
## 183  2008-06-16  7.222566
## 184  2008-06-17  7.356918
## 185  2008-06-18  7.242798
## 186  2008-06-19  7.223296
## 187  2008-06-20  7.163172
## 188  2008-06-21  7.241366
## 189  2008-06-22  6.986566
## 190  2008-06-23  6.963190
## 191  2008-06-24  7.250636
## 192  2008-06-25  7.160846
## 193  2008-06-26  7.132498
## 194  2008-06-27  7.091742
## 195  2008-06-28  7.012115
## 196  2008-06-29  6.857514
## 197  2008-06-30  6.827629
## 198  2008-07-02  7.130099
## 199  2008-07-03  7.277248
## 200  2008-07-04  7.038784
## 201  2008-07-05  6.890609
## 202  2008-07-06  6.957497
## 203  2008-07-07  7.295735
## 204  2008-07-08  7.497207
## 205  2008-07-09  7.310550
## 206  2008-07-10  7.204893
## 207  2008-07-11  7.222566
## 208  2008-07-12  7.257708
## 209  2008-08-01  7.425954
## 210  2008-08-02  7.117206
## 211  2008-08-03  7.249926
## 212  2008-08-04  8.276903
## 213  2008-08-05  7.606387
## 214  2008-08-06  7.643962
## 215  2008-08-07  8.012350
## 216  2008-08-08  7.930206
## 217  2008-08-09  7.508787
## 218  2008-08-10  7.521318
## 219  2008-08-11  7.589842
## 220  2008-08-12  7.500529
## 221  2008-08-13  7.370231
## 222  2008-08-14  7.385231
## 223  2008-08-15  7.302496
## 224  2008-08-16  7.275172
## 225  2008-08-17  7.392032
## 226  2008-08-18  7.516977
## 227  2008-08-19  7.909122
## 228  2008-08-20  7.723120
## 229  2008-08-21  7.670429
## 230  2008-08-22  7.629004
## 231  2008-08-23  7.430707
## 232  2008-08-24  7.579679
## 233  2008-08-25  7.948385
## 234  2008-08-26  7.795647
## 235  2008-08-27  8.007367
## 236  2008-08-28  7.790696
## 237  2008-08-29  7.832808
## 238  2008-08-30  7.514800
## 239  2008-08-31  7.627544
## 240  2008-09-01  7.855157
## 241  2008-09-02  7.964851
## 242  2008-09-03  7.745868
## 243  2008-09-04  8.080856
## 244  2008-09-05  8.259976
## 245  2008-09-06  7.769801
## 246  2008-09-07  8.177516
## 247  2008-09-08  9.281730
## 248  2008-09-09  8.338545
## 249  2008-09-10  7.830426
## 250  2008-09-11  7.808729
## 251  2008-09-12  7.816820
## 252  2008-09-13  7.554859
## 253  2008-09-14  8.555067
## 254  2008-09-15  8.207947
## 255  2008-09-16  8.083637
## 256  2008-09-17  7.791110
## 257  2008-09-18  7.670895
## 258  2008-09-19  7.640123
## 259  2008-09-20  7.550135
## 260  2008-09-21  8.249314
## 261  2008-09-22  8.304000
## 262  2008-09-23  8.126814
## 263  2008-09-24  7.706163
## 264  2008-09-25  7.663877
## 265  2008-09-26  7.526718
## 266  2008-09-27  7.925880
## 267  2008-09-28  7.921536
## 268  2008-09-29  8.033983
## 269  2008-09-30  7.725771
## 270  2008-10-01  7.694393
## 271  2008-10-02  7.449498
## 272  2008-10-03  7.391415
## 273  2008-10-04  7.346010
## 274  2008-10-05  8.101375
## 275  2008-10-06  8.156510
## 276  2008-10-07  7.971086
## 277  2008-10-08  7.872836
## 278  2008-10-09  7.635304
## 279  2008-10-10  7.587817
## 280  2008-10-11  7.342132
## 281  2008-10-12  8.177516
## 282  2008-10-13  8.340933
## 283  2008-10-14  8.476580
## 284  2008-10-15  7.873598
## 285  2008-10-16  7.717351
## 286  2008-10-17  7.490529
## 287  2008-10-18  7.375882
## 288  2008-10-19  8.075583
## 289  2008-10-20  8.165364
## 290  2008-10-23  7.585281
## 291  2008-10-24  7.607381
## 292  2008-10-25  7.267525
## 293  2008-10-26  8.040125
## 294  2008-10-27  8.109225
## 295  2008-10-28  8.806873
## 296  2008-10-29  7.747165
## 297  2008-10-30  7.480992
## 298  2008-10-31  7.346655
## 299  2008-11-01  7.247081
## 300  2008-11-02  7.938089
## 301  2008-11-03  9.035630
## 302  2008-11-04  8.041091
## 303  2008-11-05  7.406103
## 304  2008-11-06  7.973844
## 305  2008-11-07  7.768110
## 306  2008-11-08  7.471363
## 307  2008-11-09  8.030084
## 308  2008-11-10  8.729397
## 309  2008-11-11  7.937017
## 310  2008-11-12  7.665285
## 311  2008-11-13  7.580189
## 312  2008-11-14  7.710653
## 313  2008-11-15  7.261225
## 314  2008-11-16  8.046549
## 315  2008-11-17  8.093462
## 316  2008-11-18  7.767264
## 317  2008-11-19  7.496652
## 318  2008-11-20  7.552237
## 319  2008-11-21  7.497207
## 320  2008-11-22  7.312553
## 321  2008-11-23  7.938802
## 322  2008-11-24  9.058703
## 323  2008-11-25  8.194229
## 324  2008-11-26  7.519150
## 325  2008-11-27  7.551187
## 326  2008-11-28  7.713785
## 327  2008-11-29  7.605890
## 328  2008-11-30  8.499029
## 329  2008-12-01  8.291797
## 330  2008-12-02  7.894691
## 331  2008-12-03  7.790282
## 332  2008-12-04  7.655391
## 333  2008-12-05  7.610358
## 334  2008-12-06  7.531016
## 335  2008-12-07  8.231376
## 336  2008-12-08  8.006701
## 337  2008-12-09  7.858641
## 338  2008-12-10  7.697121
## 339  2008-12-11  7.595890
## 340  2008-12-12  7.735870
## 341  2008-12-13  7.351158
## 342  2008-12-14  8.031385
## 343  2008-12-15  8.394347
## 344  2008-12-16  7.823646
## 345  2008-12-17  8.086718
## 346  2008-12-18  7.771489
## 347  2008-12-19  8.688959
## 348  2008-12-20  7.747165
## 349  2008-12-21  7.960673
## 350  2008-12-22  8.624612
## 351  2008-12-23  7.996654
## 352  2008-12-24  7.620705
## 353  2008-12-25  7.431892
## 354  2008-12-26  7.462789
## 355  2008-12-27  7.448916
## 356  2008-12-28  8.251403
## 357  2008-12-29  8.555259
## 358  2008-12-30  8.315811
## 359  2008-12-31  8.309923
## 360  2009-01-01  7.758761
## 361  2009-01-02  8.808220
## 362  2009-01-03  9.121946
## 363  2009-01-04 10.153818
## 364  2009-01-05  9.267854
## 365  2009-01-06  8.434246
## 366  2009-01-07  8.137688
## 367  2009-01-08  8.044947
## 368  2009-01-09  8.228978
## 369  2009-01-10  8.141190
## 370  2009-01-11  9.215626
## 371  2009-01-12  8.732788
## 372  2009-01-13  8.510169
## 373  2009-01-14  8.104099
## 374  2009-01-15  7.950150
## 375  2009-01-16  7.852050
## 376  2009-01-17  7.656337
## 377  2009-01-18  8.044305
## 378  2009-01-19  8.801018
## 379  2009-01-20  7.829630
## 380  2009-01-21  7.777374
## 381  2009-01-22  7.935230
## 382  2009-01-23  7.672292
## 383  2009-01-24  7.388328
## 384  2009-01-25  7.511525
## 385  2009-01-26  7.663408
## 386  2009-01-27  7.789455
## 387  2009-01-28  7.807917
## 388  2009-01-29  7.824846
## 389  2009-01-30  7.906547
## 390  2009-01-31  7.702104
## 391  2009-02-01  8.477620
## 392  2009-02-02  9.149528
## 393  2009-02-03  8.062118
## 394  2009-02-04  8.066521
## 395  2009-02-05  8.059592
## 396  2009-02-06  8.049427
## 397  2009-02-07  7.762171
## 398  2009-02-08  8.097731
## 399  2009-02-09  8.018296
## 400  2009-02-10  7.616776
## 401  2009-02-11  7.842671
## 402  2009-02-12  7.768533
## 403  2009-02-13  7.530480
## 404  2009-02-14  7.332369
## 405  2009-02-15  7.224025
## 406  2009-02-16  7.416378
## 407  2009-02-17  7.427144
## 408  2009-02-18  7.397562
## 409  2009-02-19  7.495542
## 410  2009-02-20  7.399398
## 411  2009-02-21  7.008505
## 412  2009-02-22  7.118016
## 413  2009-02-23  7.483807
## 414  2009-02-24  7.571474
## 415  2009-02-25  7.648263
## 416  2009-02-26  7.474205
## 417  2009-02-27  7.472501
## 418  2009-02-28  7.211557
## 419  2009-03-01  7.343426
## 420  2009-03-02  7.482119
## 421  2009-03-03  7.410952
## 422  2009-03-04  7.403061
## 423  2009-03-05  7.452982
## 424  2009-03-06  7.423568
## 425  2009-03-07  7.085064
## 426  2009-03-08  7.210818
## 427  2009-03-09  7.356280
## 428  2009-03-10  7.304516
## 429  2009-03-11  7.465655
## 430  2009-03-12  7.869019
## 431  2009-03-13  7.248504
## 432  2009-03-14  7.078342
## 433  2009-03-15  7.221105
## 434  2009-03-16  7.334329
## 435  2009-03-17  7.292337
## 436  2009-03-18  7.299121
## 437  2009-03-19  7.283448
## 438  2009-03-20  7.301822
## 439  2009-03-21  7.062192
## 440  2009-03-22  7.181592
## 441  2009-03-23  7.505492
## 442  2009-03-24  7.874739
## 443  2009-03-25  7.578657
## 444  2009-03-26  7.367077
## 445  2009-03-27  7.257003
## 446  2009-03-28  7.056175
## 447  2009-03-29  7.502738
## 448  2009-03-30  7.443078
## 449  2009-03-31  7.481556
## 450  2009-04-01  7.482119
## 451  2009-04-02  7.519150
## 452  2009-04-03  7.659643
## 453  2009-04-04  7.244228
## 454  2009-04-05  7.232733
## 455  2009-04-06  7.342132
## 456  2009-04-07  7.421178
## 457  2009-04-08  7.492203
## 458  2009-04-09  7.315218
## 459  2009-04-10  7.141245
## 460  2009-04-11  7.009409
## 461  2009-04-12  7.087574
## 462  2009-04-13  7.304516
## 463  2009-04-14  7.374629
## 464  2009-04-15  7.512618
## 465  2009-04-16  7.517521
## 466  2009-04-17  7.374002
## 467  2009-04-18  7.141245
## 468  2009-04-19  7.161622
## 469  2009-04-20  7.484930
## 470  2009-04-21  7.512618
## 471  2009-04-22  7.444833
## 472  2009-04-23  7.474205
## 473  2009-04-24  7.671827
## 474  2009-04-25  7.842279
## 475  2009-04-26  7.924072
## 476  2009-04-27  7.828436
## 477  2009-04-28  7.586804
## 478  2009-04-29  7.629976
## 479  2009-04-30  7.709757
## 480  2009-05-01  7.526718
## 481  2009-05-02  7.193686
## 482  2009-05-03  7.257708
## 483  2009-05-04  7.454141
## 484  2009-05-05  7.481556
## 485  2009-05-06  7.559038
## 486  2009-05-07  7.444833
## 487  2009-05-08  7.337588
## 488  2009-05-09  7.135687
## 489  2009-05-10  7.085064
## 490  2009-05-11  7.272398
## 491  2009-05-12  7.510978
## 492  2009-05-13  7.498870
## 493  2009-05-14  7.444249
## 494  2009-05-15  7.403061
## 495  2009-05-16  6.916715
## 496  2009-05-17  6.977281
## 497  2009-05-18  7.482682
## 498  2009-05-19  7.413970
## 499  2009-05-20  7.372118
## 500  2009-05-21  7.333676
## 501  2009-05-22  7.395108
## 502  2009-05-23  7.036148
## 503  2009-05-24  6.874198
## 504  2009-05-25  6.984716
## 505  2009-05-26  7.455877
## 506  2009-05-27  7.494986
## 507  2009-05-28  7.331060
## 508  2009-05-29  7.104965
## 509  2009-05-30  6.993933
## 510  2009-05-31  6.930495
## 511  2009-06-01  7.218177
## 512  2009-06-02  7.475906
## 513  2009-06-03  7.364547
## 514  2009-06-04  7.239933
## 515  2009-06-05  7.309212
## 516  2009-06-06  7.138867
## 517  2009-06-07  6.972606
## 518  2009-06-08  7.188413
## 519  2009-06-09  7.334982
## 520  2009-06-10  7.334329
## 521  2009-06-11  7.432484
## 522  2009-06-12  7.391415
## 523  2009-06-13  6.961296
## 524  2009-06-14  7.021976
## 525  2009-06-15  7.213768
## 526  2009-06-16  7.509883
## 527  2009-06-17  7.328437
## 528  2009-06-18  7.496652
## 529  2009-06-19  7.200425
## 530  2009-06-20  7.084226
## 531  2009-06-21  7.149132
## 532  2009-06-22  7.256297
## 533  2009-06-23  7.198184
## 534  2009-06-24  7.288928
## 535  2009-06-25  7.128496
## 536  2009-06-26  7.082549
## 537  2009-06-27  6.822197
## 538  2009-06-28  6.947937
## 539  2009-06-29  7.112327
## 540  2009-06-30  7.199678
## 541  2009-07-01  7.317212
## 542  2009-07-02  7.098376
## 543  2009-07-03  7.044905
## 544  2009-07-04  7.304516
## 545  2009-07-05  7.793587
## 546  2009-07-06  7.805475
## 547  2009-07-07  7.483244
## 548  2009-07-08  7.356918
## 549  2009-07-09  7.507141
## 550  2009-07-10  7.375256
## 551  2009-07-11  7.196687
## 552  2009-07-12  7.223296
## 553  2009-07-13  7.352441
## 554  2009-07-14  7.317212
## 555  2009-07-15  7.444249
## 556  2009-07-16  7.355641
## 557  2009-07-17  7.324490
## 558  2009-07-18  7.214504
## 559  2009-07-19  7.284135
## 560  2009-07-20  7.540090
## 561  2009-07-21  7.474772
## 562  2009-07-22  7.829233
## 563  2009-07-23  7.681099
## 564  2009-07-24  7.729735
## 565  2009-07-25  7.303170
## 566  2009-07-26  7.282074
## 567  2009-07-27  7.485492
## 568  2009-07-28  7.618742
## 569  2009-07-29  7.693937
## 570  2009-07-30  7.539559
## 571  2009-07-31  7.438384
## 572  2009-08-01  7.273786
## 573  2009-08-02  7.355641
## 574  2009-08-03  7.658228
## 575  2009-08-04  7.843456
## 576  2009-08-05  8.368461
## 577  2009-08-06  8.172164
## 578  2009-08-07  7.811568
## 579  2009-08-08  7.575072
## 580  2009-08-09  7.658700
## 581  2009-08-10  7.866339
## 582  2009-08-11  7.781139
## 583  2009-08-12  7.754910
## 584  2009-08-13  7.708860
## 585  2009-08-14  8.207129
## 586  2009-08-15  7.711549
## 587  2009-08-16  7.734559
## 588  2009-08-17  7.967627
## 589  2009-08-18  8.403801
## 590  2009-08-19  8.292799
## 591  2009-08-20  7.985484
## 592  2009-08-21  8.671801
## 593  2009-08-22  7.782390
## 594  2009-08-23  7.786967
## 595  2009-08-24  7.946618
## 596  2009-08-25  8.173575
## 597  2009-08-26  7.809541
## 598  2009-08-27  7.803027
## 599  2009-08-28  8.051341
## 600  2009-08-29  7.973155
## 601  2009-08-30  7.869019
## 602  2009-08-31  8.162516
## 603  2009-09-01  8.040125
## 604  2009-09-02  7.963460
## 605  2009-09-03  7.838343
## 606  2009-09-04  7.913155
## 607  2009-09-05  7.953318
## 608  2009-09-06  8.076205
## 609  2009-09-07  7.982416
## 610  2009-09-08  8.128585
## 611  2009-09-09  7.954723
## 612  2009-09-10  8.110127
## 613  2009-09-11  8.213653
## 614  2009-09-12  8.046870
## 615  2009-09-13  8.924257
## 616  2009-09-14  8.617220
## 617  2009-09-15  8.519590
## 618  2009-09-16  8.014336
## 619  2009-09-17  8.057694
## 620  2009-09-18  8.104401
## 621  2009-09-19  7.993958
## 622  2009-09-20  8.431853
## 623  2009-09-21  9.738200
## 624  2009-09-22 10.179982
## 625  2009-09-24  8.361942
## 626  2009-09-28  9.948843
## 627  2009-09-29  8.759041
## 628  2009-09-30  8.251664
## 629  2009-10-01  8.078688
## 630  2009-10-02  8.173575
## 631  2009-10-03  7.889084
## 632  2009-10-04  9.099856
## 633  2009-10-05  9.406565
## 634  2009-10-06  9.164401
## 635  2009-10-07  8.487352
## 636  2009-10-08  8.431417
## 637  2009-10-09  8.277666
## 638  2009-10-10  8.312135
## 639  2009-10-11  8.790117
## 640  2009-10-12 10.280039
## 641  2009-10-13  9.075780
## 642  2009-10-17  8.699181
## 643  2009-10-18  9.086590
## 644  2009-10-19  8.861492
## 645  2009-10-20  8.544419
## 646  2009-10-21  8.447629
## 647  2009-10-22  8.252707
## 648  2009-10-23  8.109826
## 649  2009-10-24  8.136811
## 650  2009-10-25  8.726806
## 651  2009-10-26  9.382696
## 652  2009-10-27  8.578288
## 653  2009-10-28  8.238801
## 654  2009-10-29  8.122371
## 655  2009-10-30  8.055158
## 656  2009-10-31  7.832411
## 657  2009-11-01  8.897546
## 658  2009-11-02  8.725670
## 659  2009-11-03  8.564077
## 660  2009-11-04  8.219057
## 661  2009-11-05  8.147578
## 662  2009-11-06  8.001355
## 663  2009-11-07  7.789455
## 664  2009-11-08  8.811950
## 665  2009-11-09  9.002209
## 666  2009-11-10  8.593043
## 667  2009-11-11  8.281977
## 668  2009-11-12  8.465057
## 669  2009-11-13  8.494743
## 670  2009-11-14  8.405144
## 671  2009-11-16 10.558699
## 672  2009-11-17  9.124565
## 673  2009-11-18  8.731821
## 674  2009-11-19  8.528924
## 675  2009-11-20  8.505121
## 676  2009-11-21  8.276395
## 677  2009-11-23  9.123911
## 678  2009-11-24  8.585973
## 679  2009-11-25  8.315566
## 680  2009-11-26  8.661120
## 681  2009-11-27  8.925720
## 682  2009-11-28  8.441391
## 683  2009-11-29  9.227787
## 684  2009-11-30  9.264734
## 685  2009-12-01  9.274910
## 686  2009-12-02  8.392990
## 687  2009-12-03  8.585226
## 688  2009-12-04  8.423761
## 689  2009-12-05  8.337827
## 690  2009-12-06  9.059750
## 691  2009-12-07  9.298260
## 692  2009-12-08  8.761863
## 693  2009-12-09  8.507547
## 694  2009-12-10  8.399310
## 695  2009-12-11  8.523573
## 696  2009-12-12  8.379539
## 697  2009-12-13  9.091106
## 698  2009-12-14  9.761982
## 699  2009-12-15  8.929568
## 700  2009-12-16  8.530702
## 701  2009-12-17  8.587092
## 702  2009-12-18  9.797849
## 703  2009-12-19  8.664751
## 704  2009-12-20  9.172327
## 705  2009-12-21  9.201401
## 706  2009-12-22  9.330521
## 707  2009-12-23  8.684570
## 708  2009-12-24  8.502486
## 709  2009-12-25  8.288786
## 710  2009-12-26  8.298042
## 711  2009-12-27  9.162934
## 712  2009-12-28  9.547955
## 713  2009-12-29  9.017241
## 714  2009-12-30  8.784928
## 715  2009-12-31  8.386629
## 716  2010-01-01  8.334472
## 717  2010-01-02  8.536015
## 718  2010-01-03  8.708640
## 719  2010-01-04  8.730044
## 720  2010-01-05  8.375630
## 721  2010-01-06  8.318986
## 722  2010-01-07  8.464425
## 723  2010-01-08  8.597297
## 724  2010-01-09  8.922792
## 725  2010-01-10  9.491677
## 726  2010-01-11  9.210140
## 727  2010-01-12  8.677951
## 728  2010-01-13  8.602269
## 729  2010-01-14  8.614501
## 730  2010-01-15  8.658866
## 731  2010-01-16  8.779404
## 732  2010-01-17 11.007933
## 733  2010-01-18  9.753246
## 734  2010-01-19  9.225130
## 735  2010-01-20  9.017726
## 736  2010-01-21  8.936956
## 737  2010-01-22  9.009325
## 738  2010-01-25 11.484063
## 739  2010-01-26 10.264234
## 740  2010-01-27  9.694432
## 741  2010-01-28  9.440420
## 742  2010-01-29  9.353748
## 743  2010-01-30  9.228475
## 744  2010-01-31  9.303922
## 745  2010-02-01 10.240174
## 746  2010-02-02  9.915959
## 747  2010-02-03 10.111517
## 748  2010-02-04  9.858595
## 749  2010-02-05 10.119002
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## 751  2010-02-07 11.191452
## 752  2010-02-09 10.463332
## 753  2010-02-10  9.654064
## 754  2010-02-11  9.119759
## 755  2010-02-12  8.795734
## 756  2010-02-13  8.448486
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## 758  2010-02-15  8.218518
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## 760  2010-02-17  8.008033
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## 762  2010-02-19  7.928766
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## 764  2010-02-21  7.866339
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## 766  2010-02-24  8.310415
## 767  2010-02-25  7.828038
## 768  2010-02-26  7.873598
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## 773  2010-03-03  7.749753
## 774  2010-03-04  8.068090
## 775  2010-03-05  8.725832
## 776  2010-03-06  7.654443
## 777  2010-03-07  7.603399
## 778  2010-03-08  7.753194
## 779  2010-03-09  7.770223
## 780  2010-03-10  7.631432
## 781  2010-03-11  7.543803
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## 784  2010-03-14  7.510978
## 785  2010-03-15  7.674617
## 786  2010-03-16  7.712891
## 787  2010-03-17  7.701652
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## 790  2010-03-20  7.403670
## 791  2010-03-21  7.466228
## 792  2010-03-22  7.612337
## 793  2010-03-23  7.801800
## 794  2010-03-24  8.028781
## 795  2010-03-25  7.730175
## 796  2010-03-26  7.639642
## 797  2010-03-27  7.563201
## 798  2010-03-28  7.486613
## 799  2010-03-29  7.507690
## 800  2010-03-30  7.653969
## 801  2010-03-31  7.612831
## 802  2010-04-01  7.454141
## 803  2010-04-02  7.367077
## 804  2010-04-03  7.452982
## 805  2010-04-04  7.478735
## 806  2010-04-05  7.985144
## 807  2010-04-06  7.821643
## 808  2010-04-07  7.660585
## 809  2010-04-08  7.559559
## 810  2010-04-09  7.576610
## 811  2010-04-10  7.450080
## 812  2010-04-11  7.498870
## 813  2010-04-12  7.515889
## 814  2010-04-13  7.608374
## 815  2010-04-14  7.586296
## 816  2010-04-15  7.680637
## 817  2010-04-16  7.784889
## 818  2010-04-17  7.552237
## 819  2010-04-18  7.598900
## 820  2010-04-19  7.648263
## 821  2010-04-20  7.669962
## 822  2010-04-21  7.855545
## 823  2010-04-22  8.096513
## 824  2010-04-23  8.921057
## 825  2010-04-24  8.398635
## 826  2010-04-25  7.988204
## 827  2010-04-26  8.002694
## 828  2010-04-27  8.073091
## 829  2010-04-28  7.983099
## 830  2010-04-29  7.846199
## 831  2010-04-30  7.786552
## 832  2010-05-01  7.444833
## 833  2010-05-02  7.542213
## 834  2010-05-03  7.642524
## 835  2010-05-04  7.651120
## 836  2010-05-05  7.511525
## 837  2010-05-06  7.676937
## 838  2010-05-07  7.991254
## 839  2010-05-08  7.441907
## 840  2010-05-09  7.383989
## 841  2010-05-10  7.605890
## 842  2010-05-11  7.586804
## 843  2010-05-12  7.621195
## 844  2010-05-13  7.295735
## 845  2010-05-14  7.488853
## 846  2010-05-15  7.273093
## 847  2010-05-16  7.346655
## 848  2010-05-17  7.473637
## 849  2010-05-18  7.355641
## 850  2010-05-19  7.228388
## 851  2010-05-20  7.396949
## 852  2010-05-21  7.475339
## 853  2010-05-22  7.409742
## 854  2010-05-23  7.346010
## 855  2010-05-24  7.407924
## 856  2010-05-25  7.383989
## 857  2010-05-26  7.380879
## 858  2010-05-27  7.206377
## 859  2010-05-28  7.093405
## 860  2010-05-29  7.109879
## 861  2010-05-30  7.055313
## 862  2010-05-31  7.116394
## 863  2010-06-01  7.192182
## 864  2010-06-02  7.249215
## 865  2010-06-03  7.419381
## 866  2010-06-04  7.562162
## 867  2010-06-05  7.433075
## 868  2010-06-06  7.285507
## 869  2010-06-07  7.935587
## 870  2010-06-08  9.019543
## 871  2010-06-09  7.225481
## 872  2010-06-10  7.027315
## 873  2010-06-11  6.799056
## 874  2010-06-12  5.446737
## 875  2010-06-13  5.323010
## 876  2010-06-14  5.262690
## 877  2010-06-15  6.306275
## 878  2010-06-16  6.652863
## 879  2010-06-17  7.219642
## 880  2010-06-18  7.388328
## 881  2010-06-19  7.138867
## 882  2010-06-20  7.043160
## 883  2010-06-21  7.206377
## 884  2010-06-22  7.029973
## 885  2010-06-23  7.007601
## 886  2010-06-24  6.918695
## 887  2010-06-25  6.884487
## 888  2010-06-27  6.137727
## 889  2010-06-29  7.206377
## 890  2010-06-30  7.137278
## 891  2010-07-01  7.054450
## 892  2010-07-02  7.112327
## 893  2010-07-03  6.926577
## 894  2010-07-04  6.814543
## 895  2010-07-06  7.355002
## 896  2010-07-11  7.131699
## 897  2010-07-12  7.077498
## 898  2010-07-13  7.242082
## 899  2010-07-14  7.247081
## 900  2010-07-15  7.646354
## 901  2010-07-16  7.456455
## 902  2010-07-17  7.309881
## 903  2010-07-18  7.237778
## 904  2010-07-19  7.275172
## 905  2010-07-20  7.469084
## 906  2010-07-21  7.450661
## 907  2010-07-22  8.127405
## 908  2010-07-23  7.774856
## 909  2010-07-24  7.521318
## 910  2010-07-25  7.549609
## 911  2010-07-26  7.949797
## 912  2010-07-27  7.797702
## 913  2010-07-28  7.799753
## 914  2010-07-29  7.900266
## 915  2010-07-30  7.858254
## 916  2010-07-31  7.941651
## 917  2010-08-01  7.671361
## 918  2010-08-02  8.135347
## 919  2010-08-03  8.687779
## 920  2010-08-04  8.453188
## 921  2010-08-05  8.064636
## 922  2010-08-06  8.009363
## 923  2010-08-07  7.877397
## 924  2010-08-08  7.855157
## 925  2010-08-09  8.140898
## 926  2010-08-10  7.921173
## 927  2010-08-11  7.970740
## 928  2010-08-12  7.965198
## 929  2010-08-13  8.134761
## 930  2010-08-14  7.798523
## 931  2010-08-15  8.307706
## 932  2010-08-16  8.280711
## 933  2010-08-17  8.744488
## 934  2010-08-18  8.591373
## 935  2010-08-19  8.440528
## 936  2010-08-20  8.509766
## 937  2010-08-21  8.355145
## 938  2010-08-22  8.280964
## 939  2010-08-23  8.440528
## 940  2010-08-24  8.313852
## 941  2010-08-25  8.080856
## 942  2010-08-26  8.185907
## 943  2010-08-27  8.856803
## 944  2010-08-28  8.073091
## 945  2010-08-29  8.141481
## 946  2010-08-30  8.187855
## 947  2010-08-31  8.115222
## 948  2010-09-01  8.159089
## 949  2010-09-02  8.204398
## 950  2010-09-03  8.285009
## 951  2010-09-04  8.082711
## 952  2010-09-05  8.245647
## 953  2010-09-06  8.222016
## 954  2010-09-07  8.451267
## 955  2010-09-08  8.551981
## 956  2010-09-09  8.625150
## 957  2010-09-10  9.131946
## 958  2010-09-11  8.339979
## 959  2010-09-12  9.866201
## 960  2010-09-13  9.270777
## 961  2010-09-14  8.771835
## 962  2010-09-15  8.494743
## 963  2010-09-16  8.616314
## 964  2010-09-17  8.947806
## 965  2010-09-18  9.075780
## 966  2010-09-19  9.500469
## 967  2010-09-20 11.426103
## 968  2010-09-21  9.295508
## 969  2010-09-22  8.617220
## 970  2010-09-23  8.476996
## 971  2010-09-24  8.327726
## 972  2010-09-25  8.303752
## 973  2010-09-26  9.330432
## 974  2010-09-27  9.416134
## 975  2010-09-28  8.922925
## 976  2010-09-29  8.445912
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## 1884 2013-03-30  7.768110
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## 1900 2013-04-15  7.486613
## 1901 2013-04-16  7.574045
## 1902 2013-04-17  7.568896
## 1903 2013-04-18  7.639642
## 1904 2013-04-19  7.853216
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## 1906 2013-04-21  7.536364
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## 1908 2013-04-23  7.731931
## 1909 2013-04-24  8.012018
## 1910 2013-04-25  7.980366
## 1911 2013-04-26  8.171317
## 1912 2013-04-27  7.977968
## 1913 2013-04-28  7.794823
## 1914 2013-04-29  8.304247
## 1915 2013-04-30  8.056427
## 1916 2013-05-01  7.777793
## 1917 2013-05-02  8.228978
## 1918 2013-05-03  7.900637
## 1919 2013-05-04  7.461640
## 1920 2013-05-05  7.549083
## 1921 2013-05-06  7.816820
## 1922 2013-05-07  7.722235
## 1923 2013-05-08  7.715570
## 1924 2013-05-09  7.726213
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## 1926 2013-05-11  7.265430
## 1927 2013-05-12  7.301148
## 1928 2013-05-13  7.474205
## 1929 2013-05-14  7.588830
## 1930 2013-05-15  7.610853
## 1931 2013-05-16  7.647786
## 1932 2013-05-17  7.601902
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## 1943 2013-05-28  7.450661
## 1944 2013-05-29  7.551187
## 1945 2013-05-30  7.613325
## 1946 2013-05-31  7.427144
## 1947 2013-06-01  7.350516
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## 1949 2013-06-03  7.434848
## 1950 2013-06-04  7.537430
## 1951 2013-06-05  7.352441
## 1952 2013-06-06  7.282074
## 1953 2013-06-07  7.303170
## 1954 2013-06-08  7.293698
## 1955 2013-06-09  7.229839
## 1956 2013-06-10  7.575072
## 1957 2013-06-11  7.974189
## 1958 2013-06-12  7.615791
## 1959 2013-06-13  7.474205
## 1960 2013-06-14  7.334329
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## 1962 2013-06-16  7.404888
## 1963 2013-06-17  7.424762
## 1964 2013-06-18  7.470224
## 1965 2013-06-19  7.367709
## 1966 2013-06-20  7.284135
## 1967 2013-06-21  7.325808
## 1968 2013-06-22  7.290975
## 1969 2013-06-23  7.191429
## 1970 2013-06-24  7.289611
## 1971 2013-06-25  7.332369
## 1972 2013-06-26  7.395722
## 1973 2013-06-27  7.567346
## 1974 2013-06-28  7.621195
## 1975 2013-06-29  7.268920
## 1976 2013-06-30  7.269617
## 1977 2013-07-01  7.307873
## 1978 2013-07-02  7.281386
## 1979 2013-07-03  7.321189
## 1980 2013-07-04  7.512071
## 1981 2013-07-05  7.500529
## 1982 2013-07-06  7.113142
## 1983 2013-07-07  7.142037
## 1984 2013-07-08  7.323831
## 1985 2013-07-09  7.428927
## 1986 2013-07-10  7.528869
## 1987 2013-07-11  7.419980
## 1988 2013-07-12  7.473069
## 1989 2013-07-13  7.337588
## 1990 2013-07-14  7.354362
## 1991 2013-07-15  7.582738
## 1992 2013-07-16  7.626083
## 1993 2013-07-17  7.759614
## 1994 2013-07-18  7.940584
## 1995 2013-07-19  7.590852
## 1996 2013-07-20  7.418181
## 1997 2013-07-21  7.411556
## 1998 2013-07-22  7.597898
## 1999 2013-07-24  6.635947
## 2000 2013-07-25  7.647309
## 2001 2013-07-26  7.827640
## 2002 2013-07-27  7.633854
## 2003 2013-07-28  8.530307
## 2004 2013-07-29  8.529517
## 2005 2013-07-30  7.851272
## 2006 2013-07-31  7.795647
## 2007 2013-08-01  7.582229
## 2008 2013-08-02  7.438972
## 2009 2013-08-03  7.638680
## 2010 2013-08-04  7.527256
## 2011 2013-08-05  7.724888
## 2012 2013-08-06  7.913521
## 2013 2013-08-07  8.659560
## 2014 2013-08-08  8.295798
## 2015 2013-08-09  8.132413
## 2016 2013-08-10  7.925519
## 2017 2013-08-11  7.828436
## 2018 2013-08-12  7.844241
## 2019 2013-08-13  7.776954
## 2020 2013-08-14  7.766841
## 2021 2013-08-15  7.789869
## 2022 2013-08-16  7.693937
## 2023 2013-08-17  7.715570
## 2024 2013-08-18  8.152774
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## 2027 2013-08-21  7.809541
## 2028 2013-08-22  7.819234
## 2029 2013-08-23  7.812378
## 2030 2013-08-24  7.545390
## 2031 2013-08-25  8.474286
## 2032 2013-08-26  7.791936
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## 2560 2015-02-08  7.812783
## 2561 2015-02-09  7.931285
## 2562 2015-02-10  8.414496
## 2563 2015-02-11  8.156510
## 2564 2015-02-12  7.857094
## 2565 2015-02-13  7.909857
## 2566 2015-02-14  7.809135
## 2567 2015-02-15  7.507690
## 2568 2015-02-16  8.203851
## 2569 2015-02-17  7.821643
## 2570 2015-02-18  7.803843
## 2571 2015-02-19  7.760893
## 2572 2015-02-20  7.703459
## 2573 2015-02-21  8.061171
## 2574 2015-02-22  7.350516
## 2575 2015-02-23  7.483807
## 2576 2015-02-24  7.540622
## 2577 2015-02-25  7.696667
## 2578 2015-02-26  7.503841
## 2579 2015-02-27  7.398174
## 2580 2015-02-28  7.042286
## 2581 2015-03-01  7.052721
## 2582 2015-03-02  7.362645
## 2583 2015-03-03  7.623153
## 2584 2015-03-04  7.795235
## 2585 2015-03-05  8.426831
## 2586 2015-03-06  7.916807
## 2587 2015-03-07  7.236339
## 2588 2015-03-08  7.206377
## 2589 2015-03-09  7.556428
## 2590 2015-03-10  7.582738
## 2591 2015-03-11  7.682943
## 2592 2015-03-12  7.606885
## 2593 2015-03-13  7.703459
## 2594 2015-03-14  7.151485
## 2595 2015-03-15  7.040536
## 2596 2015-03-16  7.338888
## 2597 2015-03-17  7.484369
## 2598 2015-03-18  7.351800
## 2599 2015-03-19  7.423568
## 2600 2015-03-20  7.291656
## 2601 2015-03-21  6.816736
## 2602 2015-03-22  6.910751
## 2603 2015-03-23  7.321189
## 2604 2015-03-24  7.991592
## 2605 2015-03-25  7.712891
## 2606 2015-03-26  7.282761
## 2607 2015-03-27  7.305860
## 2608 2015-03-28  6.905753
## 2609 2015-03-29  7.873217
## 2610 2015-03-30  7.085901
## 2611 2015-03-31  7.271009
## 2612 2015-04-01  7.213768
## 2613 2015-04-02  7.166266
## 2614 2015-04-03  7.213032
## 2615 2015-04-04  6.829794
## 2616 2015-04-05  6.801283
## 2617 2015-04-06  7.157735
## 2618 2015-04-07  7.045777
## 2619 2015-04-08  7.091742
## 2620 2015-04-09  7.234177
## 2621 2015-04-10  7.280008
## 2622 2015-04-11  6.697034
## 2623 2015-04-12  7.028201
## 2624 2015-04-13  7.174724
## 2625 2015-04-14  7.223296
## 2626 2015-04-15  7.336937
## 2627 2015-04-16  7.362011
## 2628 2015-04-17  7.263330
## 2629 2015-04-18  6.811244
## 2630 2015-04-19  7.318540
## 2631 2015-04-20  7.640123
## 2632 2015-04-21  7.405496
## 2633 2015-04-22  7.572503
## 2634 2015-04-23  7.485492
## 2635 2015-04-24  7.333023
## 2636 2015-04-25  7.205635
## 2637 2015-04-26  7.090910
## 2638 2015-04-27  7.326466
## 2639 2015-04-28  7.355641
## 2640 2015-04-29  7.463363
## 2641 2015-04-30  7.567346
## 2642 2015-05-01  7.749753
## 2643 2015-05-02  7.144407
## 2644 2015-05-03  6.899723
## 2645 2015-05-04  7.331060
## 2646 2015-05-05  7.221105
## 2647 2015-05-06  7.737616
## 2648 2015-05-07  7.363280
## 2649 2015-05-08  7.290975
## 2650 2015-05-09  7.038784
## 2651 2015-05-10  6.932448
## 2652 2015-05-11  7.305860
## 2653 2015-05-12  7.686162
## 2654 2015-05-13  7.479300
## 2655 2015-05-14  7.269617
## 2656 2015-05-15  7.309212
## 2657 2015-05-16  6.740519
## 2658 2015-05-17  6.805723
## 2659 2015-05-18  7.142827
## 2660 2015-05-19  7.186901
## 2661 2015-05-20  7.140453
## 2662 2015-05-21  8.761550
## 2663 2015-05-22  8.279443
## 2664 2015-05-23  7.437206
## 2665 2015-05-24  7.160069
## 2666 2015-05-25  7.041412
## 2667 2015-05-26  7.174724
## 2668 2015-05-27  7.412764
## 2669 2015-05-28  7.256297
## 2670 2015-05-29  7.284821
## 2671 2015-05-30  6.726233
## 2672 2015-05-31  6.932448
## 2673 2015-06-01  7.074117
## 2674 2015-06-02  7.202661
## 2675 2015-06-03  7.164720
## 2676 2015-06-04  7.067320
## 2677 2015-06-05  6.906755
## 2678 2015-06-06  6.677083
## 2679 2015-06-07  6.517671
## 2680 2015-06-08  7.043160
## 2681 2015-06-09  7.043160
## 2682 2015-06-10  6.917706
## 2683 2015-06-11  7.057898
## 2684 2015-06-12  6.855409
## 2685 2015-06-13  6.643790
## 2686 2015-06-14  6.525030
## 2687 2015-06-15  6.890609
## 2688 2015-06-16  6.926577
## 2689 2015-06-17  7.004882
## 2690 2015-06-18  6.873164
## 2691 2015-06-19  6.890609
## 2692 2015-06-20  6.442540
## 2693 2015-06-21  6.835185
## 2694 2015-06-22  7.272398
## 2695 2015-06-23  7.077498
## 2696 2015-06-24  7.344073
## 2697 2015-06-25  7.291656
## 2698 2015-06-26  7.271704
## 2699 2015-06-27  7.454720
## 2700 2015-06-28  6.692084
## 2701 2015-06-29  6.963190
## 2702 2015-06-30  7.016610
## 2703 2015-07-01  6.791221
## 2704 2015-07-02  6.820016
## 2705 2015-07-03  6.618739
## 2706 2015-07-04  6.473891
## 2707 2015-07-05  6.499787
## 2708 2015-07-06  6.859615
## 2709 2015-07-07  6.881411
## 2710 2015-07-08  6.997596
## 2711 2015-07-09  7.152269
## 2712 2015-07-10  7.196687
## 2713 2015-07-11  6.708084
## 2714 2015-07-12  6.982863
## 2715 2015-07-13  7.128496
## 2716 2015-07-14  7.089243
## 2717 2015-07-15  7.198931
## 2718 2015-07-16  8.090709
## 2719 2015-07-17  7.393878
## 2720 2015-07-18  7.050123
## 2721 2015-07-19  7.195187
## 2722 2015-07-20  7.441320
## 2723 2015-07-21  7.417580
## 2724 2015-07-22  7.474205
## 2725 2015-07-23  7.392648
## 2726 2015-07-24  7.185387
## 2727 2015-07-25  6.864848
## 2728 2015-07-26  6.834109
## 2729 2015-07-27  7.287561
## 2730 2015-07-28  7.224025
## 2731 2015-07-29  7.244228
## 2732 2015-07-30  7.306531
## 2733 2015-07-31  7.317212
## 2734 2015-08-01  6.958448
## 2735 2015-08-02  6.825460
## 2736 2015-08-03  7.181592
## 2737 2015-08-04  7.276556
## 2738 2015-08-05  7.271009
## 2739 2015-08-06  7.824446
## 2740 2015-08-07  7.419381
## 2741 2015-08-08  7.007601
## 2742 2015-08-09  7.073270
## 2743 2015-08-10  7.265430
## 2744 2015-08-11  7.602401
## 2745 2015-08-12  7.557473
## 2746 2015-08-13  7.582229
## 2747 2015-08-14  7.289611
## 2748 2015-08-15  7.330405
## 2749 2015-08-16  7.221105
## 2750 2015-08-17  7.431300
## 2751 2015-08-18  7.750184
## 2752 2015-08-19  7.629976
## 2753 2015-08-20  7.730614
## 2754 2015-08-21  7.824046
## 2755 2015-08-22  7.226209
## 2756 2015-08-23  7.477038
## 2757 2015-08-24  7.863267
## 2758 2015-08-25  7.949091
## 2759 2015-08-26  7.769801
## 2760 2015-08-27  7.579679
## 2761 2015-08-28  7.549083
## 2762 2015-08-29  7.291656
## 2763 2015-08-30  7.789869
## 2764 2015-08-31  7.656810
## 2765 2015-09-01  7.534763
## 2766 2015-09-02  7.665285
## 2767 2015-09-03  8.066521
## 2768 2015-09-04  8.149313
## 2769 2015-09-05  7.725330
## 2770 2015-09-06  7.717351
## 2771 2015-09-07  7.677864
## 2772 2015-09-08  7.895063
## 2773 2015-09-09  8.079928
## 2774 2015-09-10  8.193400
## 2775 2015-09-11  8.665096
## 2776 2015-09-12  7.844633
## 2777 2015-09-13  8.779096
## 2778 2015-09-14  9.058703
## 2779 2015-09-15  8.421783
## 2780 2015-09-16  8.072155
## 2781 2015-09-17  8.404696
## 2782 2015-09-18  9.721846
## 2783 2015-09-19  8.114025
## 2784 2015-09-20  8.430763
## 2785 2015-09-21  8.548886
## 2786 2015-09-22  8.322880
## 2787 2015-09-23  8.008366
## 2788 2015-09-24  8.119994
## 2789 2015-09-25  8.582606
## 2790 2015-09-26  7.609862
## 2791 2015-09-27  8.412055
## 2792 2015-09-28  9.541010
## 2793 2015-09-29  8.559486
## 2794 2015-09-30  8.144389
## 2795 2015-10-01  7.991254
## 2796 2015-10-02  7.885329
## 2797 2015-10-03  7.459915
## 2798 2015-10-04  8.375169
## 2799 2015-10-05  8.726806
## 2800 2015-10-06  8.075272
## 2801 2015-10-07  7.800573
## 2802 2015-10-08  7.749753
## 2803 2015-10-09  7.919720
## 2804 2015-10-10  7.356280
## 2805 2015-10-11  8.173011
## 2806 2015-10-13  8.261010
## 2807 2015-10-14  7.846590
## 2808 2015-10-15  7.740230
## 2809 2015-10-16  7.830426
## 2810 2015-10-17  7.361375
## 2811 2015-10-18  8.298788
## 2812 2015-10-19  8.741776
## 2813 2015-10-20  8.397057
## 2814 2015-10-21  7.778211
## 2815 2015-10-22  7.933797
## 2816 2015-10-23  7.860185
## 2817 2015-10-24  7.942362
## 2818 2015-10-25  8.198089
## 2819 2015-10-26  8.429018
## 2820 2015-10-27  8.056744
## 2821 2015-10-28  7.811163
## 2822 2015-10-29  7.786552
## 2823 2015-10-30  8.108623
## 2824 2015-10-31  7.621195
## 2825 2015-11-01  8.092851
## 2826 2015-11-02  9.392245
## 2827 2015-11-03  8.453188
## 2828 2015-11-04  8.094378
## 2829 2015-11-05  7.991254
## 2830 2015-11-06  8.328209
## 2831 2015-11-07  7.641084
## 2832 2015-11-08  8.486322
## 2833 2015-11-09  9.163563
## 2834 2015-11-10  8.188411
## 2835 2015-11-11  7.826443
## 2836 2015-11-12  7.960673
## 2837 2015-11-13  7.672292
## 2838 2015-11-14  7.163172
## 2839 2015-11-15  7.902118
## 2840 2015-11-16  9.634300
## 2841 2015-11-17  8.848222
## 2842 2015-11-18  8.383205
## 2843 2015-11-19  8.164510
## 2844 2015-11-20  8.052933
## 2845 2015-11-21  7.561122
## 2846 2015-11-22  8.256348
## 2847 2015-11-23  8.672828
## 2848 2015-11-24  8.306472
## 2849 2015-11-25  8.058960
## 2850 2015-11-26  7.872455
## 2851 2015-11-27  8.195334
## 2852 2015-11-28  7.591357
## 2853 2015-11-29  8.021585
## 2854 2015-11-30 12.149672
## 2855 2015-12-01 11.523044
## 2856 2015-12-02  8.711773
## 2857 2015-12-03  8.056110
## 2858 2015-12-04  8.081475
## 2859 2015-12-05  7.458763
## 2860 2015-12-06  8.014005
## 2861 2015-12-07  8.496786
## 2862 2015-12-08  7.981050
## 2863 2015-12-09  7.777793
## 2864 2015-12-10  8.260234
## 2865 2015-12-11  7.866339
## 2866 2015-12-12  7.310550
## 2867 2015-12-13  7.718241
## 2868 2015-12-14  8.319474
## 2869 2015-12-15  8.236685
## 2870 2015-12-16  7.807510
## 2871 2015-12-17  7.591862
## 2872 2015-12-18  7.528869
## 2873 2015-12-19  7.171657
## 2874 2015-12-20  7.891331
## 2875 2015-12-21  8.360071
## 2876 2015-12-22  8.110427
## 2877 2015-12-23  7.775276
## 2878 2015-12-24  7.347300
## 2879 2015-12-25  7.301822
## 2880 2015-12-26  7.120444
## 2881 2015-12-27  8.878776
## 2882 2015-12-28  9.250618
## 2883 2015-12-29  9.247925
## 2884 2015-12-30  8.391403
## 2885 2015-12-31  8.004700
## 2886 2016-01-01  7.589336
## 2887 2016-01-02  7.825245
## 2888 2016-01-03  8.249314
## 2889 2016-01-04  9.295141
## 2890 2016-01-05  8.568266
## 2891 2016-01-06  8.352554
## 2892 2016-01-07  8.295798
## 2893 2016-01-08  8.290293
## 2894 2016-01-09  7.785721
## 2895 2016-01-10  8.281724
## 2896 2016-01-11  8.470730
## 2897 2016-01-12  8.135054
## 2898 2016-01-13  8.067149
## 2899 2016-01-14  8.023552
## 2900 2016-01-15  8.021913
## 2901 2016-01-16  7.817223
## 2902 2016-01-17  9.273878
## 2903 2016-01-18 10.333775
## 2904 2016-01-19  9.125871
## 2905 2016-01-20  8.891374

The result shows that it remains the same throughout the years.

3.3 Predicting the future values

We would want to know how the views of Wikipedia changes for 1 year to January 2017. So we would use the prophet forecasting system to find out.

model2 = prophet::prophet(dataFrame2)

## Disabling daily seasonality. Run prophet with daily.seasonality=TRUE to override this.

future2 = prophet::make_future_dataframe(model2, periods=365)#It creates future dates from 21st January to 20th January 2017.
forecast2 = predict(model2, future2)#It adds 24 future values into the data frame.
tail(forecast2[c('ds', 'yhat', 'yhat_lower', 'yhat_upper')])# Only showing the last 6 future dates with predicted values.

##              ds     yhat yhat_lower yhat_upper
## 3265 2017-01-14 7.827290   7.064199   8.550221
## 3266 2017-01-15 8.209113   7.547296   8.886127
## 3267 2017-01-16 8.534106   7.867145   9.239982
## 3268 2017-01-17 8.321526   7.584073   9.030776
## 3269 2017-01-18 8.154180   7.396946   8.868041
## 3270 2017-01-19 8.166079   7.449262   8.904157

The futures dates indicate an decrease in numbers on views. This could be due to his retirement.

3.4 Graphs

3.4.1 Plots

plot(model2, forecast2,xlab="dates",ylab="Daily Views (log(y))",main="Peyton Mannings")

In this graph,the daily views is fairly constant throughout the years between around 6.5 and 10(665 and 22,026). But, in some days, there were more people visited Peyton Manning’s Wikipedia pages as high as around 12.8(362,217 views) because of his achievement and performances in one of his matches. Sometimes, the views were lower, with the lowest being 5.3(200 views).

3.4.2 Seasonality

We can further broke down into trend and 2 seasonality: weekly and yearly.

prophet::prophet_plot_components(model2, forecast2)#Graph broken down into 2 sesonalities and trend.

3.4.2.1 Trend

The trend graph started off with decrease in trends. This is because of the 2007 season of NFL have ended, meaning it may not be a point to view any NFL players during off-season. But, when 2008 season starts, it stop decreasing and remain constant. As Manning earn a MVP for his performance, trend tends to rise, even during off-season.This shows that Peyton Manning is being recognised. It remain constant after 2009 season with a little decrease, which is still higher than when observations start as he again earn his MVP. In 2011, the trend rises even more. This is because Manning is injured due to neck surgery and is left out for entire season. This was also his last lime in Indianapolis Colts before moving as free agent, so people want to know what happened to him . In 2012, the trend decreases as he moves to Denver Broncos. But in 2013, it increases again as he earn MVP yet again due to his performances in 2013 season, which helped Denver Broncos reached into Super Bowl XLVIII. After 2014, it gradually decreases. This is due to his retirement in 2016. This shows that change in trend depends on his achievement and performances. #### 3.4.2.2 Weekly seasonality

NFL games normally plays on Sundays, Mondays and Thursdays, with most games being held on Sundays. Therefore most Manning’s matches have been played on Sunday’s. This indicates that more people have visited his Wikipedia page on Monday following his Sunday’s games. As some of his matches have also played on Monday, Tuesday’s data tends to have positive trend. However, other days tend to go negative as games doesn’t normally played on these days - meaning less people looking at Manning’s Wikipedia page - with Saturday even lower as his games don’t often played on Fridays.

3.4.2.3 Yearly Seasonality

Any season of NFL start in weekend following Labor’s Day in September with a regular season and ends with Super Bowl in 2nd Sunday of February. Regular season ends in January, when play-offs began. There’s no NFL matches from after Super Bowl. So less people would look at any Wikipedia pages, including Peyton Manning, from the end of Super Bowl. Therefore, this would lead to decrease in trend. But, when pre-season starts, trends rises meaning people would then look at Manning’s Wikipedia page and rapidly increases back to positive when regular season starts. The highest peak is around the start of February where play-off season and Super Bowl take place.

3.4.3 Dynamic plots

prophet::dyplot.prophet(model2, forecast2)# Dygraph showing trends including predicted values and dates from 2016 to 2017.

## Warning: `select_()` was deprecated in dplyr 0.7.0.
## ℹ Please use `select()` instead.
## ℹ The deprecated feature was likely used in the prophet package.
##   Please report the issue at <https://github.com/facebook/prophet/issues>.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

The dygraph shows the interactive forecast of this time series. It can be use to explore the predicted value in depth by moving timeline so that we can see how the prediction goes.

3.5 Sources

Wikipedia page: https://en.wikipedia.org/wiki/Peyton_Manning

Data from GitHub: https://github.com/facebook/prophet/blob/main/examples/example_wp_log_peyton_manning.csv

4 Comparision

In Mauna Loa CO2 Concentration’s forecast, the trend tend to increase overtime whereas in Peyton Manning’s forecast, the trend do increase at start before it decreases gradually. This is because Peyton Manning’s forecast, it rely on people viewing in which people can change their habit on this, whereas in Mauna Loa’s forecast, it rely on concentration of CO2 rising in the atmosphere,in which people can’t change their habit. It’s also worth noting that people changing their habit in viewing Wikipedia pages can varied the number of daily views. Also, Mauna Loa’s forecast only observed monthly, whereas Payton Manning’s forecast does observed daily, meaning that despite very large dataset, it can give accurate result.