TimeSeries.OBeu

Kleanthis Koupidis, Charalampos Bratsas

TimeSeries.OBeu

Εstimate and return the necessary parameters for time series visualizations, used in OpenBudgets.eu. It includes functions to test stationarity (with ACF, PACF, Phillips Perron test, Augmented Dickey Fuller (ADF) test, Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test, Mann Kendall Test For Monotonic Trend and Cox and Stuart trend test), decompose, model and forecast Budget time series data of municipalities across Europe, according to the OpenBudgets.eu data model.

This package can generally be used to extract visualization parameters convert them to JSON format and use them as input in a different graphical interface. Most functions can have general use out of the OpenBudgets.eu data model. You can see detailed information here.

# install TimeSeries.OBeu- cran stable version
install.packages(TimeSeries.OBeu) 
# or
# alternatively install the development version from github
devtools::install_github("okgreece/TimeSeries.OBeu")

Load library TimeSeries.OBeu

library(TimeSeries.OBeu)

Time Series analysis in a call

ts.analysis is used to estimate autocorrelation and partial autocorrelation of input time series data, autocorrelation and partial autocorrelation of the model residuals, trend, seasonal (if exists) and remainder components, model parameters such as arima order, arima coefficients etc. and the desired forecasts with their corresponding confidence intervals.

ts.analysis returns by default a json object, if tojson parameter is FALSE returns a list object and the default forecast step is set to 1.

results = ts.analysis(Athens_executed_ts, prediction.steps = 2, tojson=TRUE) # json string format
jsonlite::prettify(results) # use prettify of jsonlite library to add indentation to the returned JSON string
## {
##     "acf.param": {
##         "acf.parameters": {
##             "acf": [
##                 1,
##                 0.5302,
##                 0.2018,
##                 -0.1397,
##                 -0.4059,
##                 -0.3556,
##                 -0.3939,
##                 -0.073,
##                 0.071,
##                 0.0676,
##                 0.0285
##             ],
##             "acf.lag": [
##                 0,
##                 1,
##                 2,
##                 3,
##                 4,
##                 5,
##                 6,
##                 7,
##                 8,
##                 9,
##                 10
##             ],
##             "confidence.interval.up": [
##                 0.5658
##             ],
##             "confidence.interval.low": [
##                 -0.5658
##             ]
##         },
##         "pacf.parameters": {
##             "pacf": [
##                 0.5302,
##                 -0.1102,
##                 -0.2817,
##                 -0.2903,
##                 0.0427,
##                 -0.2781,
##                 0.2318,
##                 -0.1163,
##                 -0.1829,
##                 -0.209
##             ],
##             "pacf.lag": [
##                 1,
##                 2,
##                 3,
##                 4,
##                 5,
##                 6,
##                 7,
##                 8,
##                 9,
##                 10
##             ],
##             "confidence.interval.up": [
##                 0.5658
##             ],
##             "confidence.interval.low": [
##                 -0.5658
##             ]
##         },
##         "acf.residuals.parameters": {
##             "acf.residuals": [
##                 1,
##                 0.8646,
##                 0.7284,
##                 0.6039,
##                 0.4589,
##                 0.3295,
##                 0.154,
##                 -0.0016,
##                 -0.1241,
##                 -0.2595,
##                 -0.3802,
##                 -0.5098,
##                 -0.6276,
##                 -0.5885,
##                 -0.5207,
##                 -0.4629
##             ],
##             "acf.residuals.lag": [
##                 0,
##                 1,
##                 2,
##                 3,
##                 4,
##                 5,
##                 6,
##                 7,
##                 8,
##                 9,
##                 10,
##                 11,
##                 12,
##                 13,
##                 14,
##                 15
##             ],
##             "confidence.interval.up": [
##                 0.5658
##             ],
##             "confidence.interval.low": [
##                 -0.5658
##             ]
##         },
##         "pacf.residuals.parameters": {
##             "pacf.residuals": [
##                 0.8646,
##                 -0.0756,
##                 -0.0325,
##                 -0.1597,
##                 -0.0335,
##                 -0.2937,
##                 -0.0528,
##                 -0.046,
##                 -0.162,
##                 -0.1372,
##                 -0.2201,
##                 -0.2078,
##                 0.4336,
##                 0.1187,
##                 -0.0519
##             ],
##             "pacf.residuals.lag": [
##                 1,
##                 2,
##                 3,
##                 4,
##                 5,
##                 6,
##                 7,
##                 8,
##                 9,
##                 10,
##                 11,
##                 12,
##                 13,
##                 14,
##                 15
##             ],
##             "confidence.interval.up": [
##                 0.5658
##             ],
##             "confidence.interval.low": [
##                 -0.5658
##             ]
##         }
##     },
##     "decomposition": {
##         "stl.plot": {
##             "trend": [
##                 488397393.1091,
##                 472512470.2805,
##                 473063423.4839,
##                 487284165.8281,
##                 519914575.4486,
##                 549044538.1581,
##                 546747322.3717,
##                 517885722.186,
##                 482561749.2963,
##                 453474237.5689,
##                 423909077.9758,
##                 393617768.3187
##             ],
##             "conf.interval.up": [
##                 525849686.8842,
##                 495462596.0604,
##                 495888427.6281,
##                 512171768.3925,
##                 545880538.4876,
##                 575706534.5412,
##                 573409318.7548,
##                 543851685.225,
##                 507449351.8607,
##                 476299241.7132,
##                 446859203.7557,
##                 431070062.0938
##             ],
##             "conf.interval.low": [
##                 450945099.334,
##                 449562344.5005,
##                 450238419.3396,
##                 462396563.2637,
##                 493948612.4097,
##                 522382541.7751,
##                 520085325.9887,
##                 491919759.147,
##                 457674146.7319,
##                 430649233.4247,
##                 400958952.1958,
##                 356165474.5436
##             ],
##             "seasonal": {
## 
##             },
##             "remainder": [
##                 3494473.6909,
##                 -6782427.4905,
##                 -360030.3839,
##                 -20859217.1881,
##                 8715868.0414,
##                 20321961.4419,
##                 -24805255.8217,
##                 12476896.984,
##                 -25628827.4663,
##                 18714394.8611,
##                 -9197723.8358,
##                 1891498.5713
##             ],
##             "time": [
##                 2004,
##                 2005,
##                 2006,
##                 2007,
##                 2008,
##                 2009,
##                 2010,
##                 2011,
##                 2012,
##                 2013,
##                 2014,
##                 2015
##             ]
##         },
##         "stl.general": {
##             "degfr": [
##                 5.4179
##             ],
##             "degfr.fitted": [
##                 5.1011
##             ],
##             "stl.degree": [
##                 2
##             ]
##         },
##         "residuals_fitted": {
##             "residuals": [
##                 3494473.6909,
##                 -6782427.4905,
##                 -360030.3839,
##                 -20859217.1881,
##                 8715868.0414,
##                 20321961.4419,
##                 -24805255.8217,
##                 12476896.984,
##                 -25628827.4663,
##                 18714394.8611,
##                 -9197723.8358,
##                 1891498.5713
##             ],
##             "fitted": [
##                 488397393.1091,
##                 472512470.2805,
##                 473063423.4839,
##                 487284165.8281,
##                 519914575.4486,
##                 549044538.1581,
##                 546747322.3717,
##                 517885722.186,
##                 482561749.2963,
##                 453474237.5689,
##                 423909077.9758,
##                 393617768.3187
##             ],
##             "time": [
##                 2004,
##                 2005,
##                 2006,
##                 2007,
##                 2008,
##                 2009,
##                 2010,
##                 2011,
##                 2012,
##                 2013,
##                 2014,
##                 2015
##             ],
##             "line": [
##                 0
##             ]
##         },
##         "compare": {
##             "resid.variance": [
##                 258964785711184
##             ],
##             "used.obs": [
##                 2004,
##                 2015,
##                 2009.5,
##                 2006.75,
##                 2012.25
##             ],
##             "loglik": [
##                 -1.42430632141151e+015
##             ],
##             "aic": [
##                 2.84861264282304e+015
##             ],
##             "bic": [
##                 2.84861264282304e+015
##             ],
##             "gcv": [
##                 789007326652162
##             ]
##         }
##     },
##     "model.param": {
##         "model": {
##             "arima.order": [
##                 2,
##                 1,
##                 0,
##                 0,
##                 1,
##                 1,
##                 0
##             ],
##             "arima.coef": [
##                 -0.2,
##                 0.304,
##                 0.1684
##             ],
##             "arima.coef.se": [
##                 0.5484,
##                 0.3034,
##                 0.5345
##             ]
##         },
##         "residuals_fitted": {
##             "residuals": [
##                 491891.5916,
##                 -24734053.8013,
##                 4848198.2869,
##                 2291242.4698,
##                 58442566.8183,
##                 45241384.4941,
##                 -65806529.3585,
##                 -2362504.0059,
##                 -56932278.3288,
##                 7600701.3147,
##                 -33386168.6854,
##                 -29710365.2918
##             ],
##             "fitted": [
##                 491399975.2084,
##                 490464096.5913,
##                 467855194.8131,
##                 464133706.1702,
##                 470187876.6717,
##                 524125115.1059,
##                 587748595.9085,
##                 532725123.1759,
##                 513865200.1588,
##                 464587931.1153,
##                 448097522.8254,
##                 425219632.1818
##             ],
##             "time": [
##                 2004,
##                 2005,
##                 2006,
##                 2007,
##                 2008,
##                 2009,
##                 2010,
##                 2011,
##                 2012,
##                 2013,
##                 2014,
##                 2015
##             ],
##             "line": [
##                 0
##             ]
##         },
##         "compare": {
##             "resid.variance": [
##                 1.96694555669531e+015
##             ],
##             "variance.coef": [
##                 [
##                     0.3007,
##                     0.0586,
##                     -0.2532
##                 ],
##                 [
##                     0.0586,
##                     0.0921,
##                     -0.029
##                 ],
##                 [
##                     -0.2532,
##                     -0.029,
##                     0.2857
##                 ]
##             ],
##             "not.used.obs": [
##                 0
##             ],
##             "used.obs": [
##                 11
##             ],
##             "loglik": [
##                 -207.6519
##             ],
##             "aic": [
##                 423.3037
##             ],
##             "bic": [
##                 424.8953
##             ],
##             "aicc": [
##                 429.9704
##             ]
##         }
##     },
##     "forecasts": {
##         "ts.model": [
##             "ARIMA(2,1,1)"
##         ],
##         "data_year": [
##             2004,
##             2005,
##             2006,
##             2007,
##             2008,
##             2009,
##             2010,
##             2011,
##             2012,
##             2013,
##             2014,
##             2015
##         ],
##         "data": [
##             491891866.8,
##             465730042.79,
##             472703393.1,
##             466424948.64,
##             528630443.49,
##             569366499.6,
##             521942066.55,
##             530362619.17,
##             456932921.83,
##             472188632.43,
##             414711354.14,
##             395509266.89
##         ],
##         "predict_time": [
##             2016,
##             2017
##         ],
##         "predict_values": [
##             376873927.6929,
##             374763602.0226
##         ],
##         "up80": [
##             433711072.7506,
##             453885516.7716
##         ],
##         "low80": [
##             320036782.6353,
##             295641687.2737
##         ],
##         "up95": [
##             463798839.8792,
##             495770128.3811
##         ],
##         "low95": [
##             289949015.5067,
##             253757075.6642
##         ]
##     }
## }
## 

ts.analysis uses internally the functions ts.stationary.test,ts.acf,ts.non.seas.decomp,ts.seasonal.decomp, ts.seasonal.model, ts.non.seas.model and ts.forecast. However, these functions can be used independently and depends on the user requirements (see package manual or vignettes).

Time series analysis on OpenBudgets.eu platform

open_spending.ts is designed to estimate and return the autocorrelation parameters, time series model parameters and the forecast parameters of OpenBudgets.eu time series datasets.

The input data must be a JSON link according to the OpenBudgets.eu data model. The user should specify the amount and time variables, future steps to be predicted (default is 1 step forward) and the arima order (if not specified the most appropriate model will be selected according to AIC value).

open_spending.ts estimates and returns the json data (that are described with the OpenBudgets.eu data model), using ts.analysis function.

#example openbudgets.eu time series data
sample.ts.data = 
'{"page":0,
"page_size": 30,
"total_cell_count": 15,
"cell": [],
"status": "ok",
"cells": [{
        "global__fiscalPeriod__28951.notation": "2002",
        "global__amount__0397f.sum": 290501420.64,
        "global__amount__0397f__CZK.sum": 9210928544.2325,
        "_count": 4805
    },
    {
        "global__fiscalPeriod__28951.notation": "2003",
        "global__amount__0397f.sum": 311242291.07,
        "global__amount__0397f__CZK.sum": 9832143974.9013,
        "_count": 4988
    },
    {
        "global__fiscalPeriod__28951.notation": "2004",
        "global__amount__0397f.sum": 5268500701.1,
        "global__amount__0397f__CZK.sum": 170688885714.24,
        "_count": 10055
    },
    {
        "global__fiscalPeriod__28951.notation": "2005",
        "global__amount__0397f.sum": 2542887761.01,
        "global__amount__0397f__CZK.sum": 77204615312.025,
        "_count": 2032
    },
    {
        "global__fiscalPeriod__28951.notation": "2006",
        "global__amount__0397f.sum": 14803951786.68,
        "global__amount__0397f__CZK.sum": 429758720367.32,
        "_count": 13632
    },
    {
        "global__fiscalPeriod__28951.notation": "2007",
        "global__amount__0397f.sum": 16188514346.44,
        "global__amount__0397f__CZK.sum": 445588857385.76,
        "_count": 22798
    },
    {
        "global__fiscalPeriod__28951.notation": "2008",
        "global__amount__0397f.sum": 18231035815.89,
        "global__amount__0397f__CZK.sum": 480643028250.12,
        "_count": 24176
    },
    {
        "global__fiscalPeriod__28951.notation": "2009",
        "global__amount__0397f.sum": 19079541164.68,
        "global__amount__0397f__CZK.sum": 511808691742.54,
        "_count": 26250
    },
    {
        "global__fiscalPeriod__28951.notation": "2010",
        "global__amount__0397f.sum": 22738650575.01,
        "global__amount__0397f__CZK.sum": 597685430364.14,
        "_count": 87667
    },
    {
        "global__fiscalPeriod__28951.notation": "2011",
        "global__amount__0397f.sum": 24961375670.57,
        "global__amount__0397f__CZK.sum": 626230992823.26,
        "_count": 134352
    },
    {
        "global__fiscalPeriod__28951.notation": "2012",
        "global__amount__0397f.sum": 261513607691.41,
        "global__amount__0397f__CZK.sum": 7030666436872.5,
        "_count": 147556
    },
    {
        "global__fiscalPeriod__28951.notation": "2013",
        "global__amount__0397f.sum": 268946402299.09,
        "global__amount__0397f__CZK.sum": 7226220232913.8,
        "_count": 150079
    },
    {
        "global__fiscalPeriod__28951.notation": "2014",
        "global__amount__0397f.sum": 255222816704.9,
        "global__amount__0397f__CZK.sum": 6907598086283.4,
        "_count": 176019
    },
    {
        "global__fiscalPeriod__28951.notation": "2015",
        "global__amount__0397f.sum": 22976062973.62,
        "global__amount__0397f__CZK.sum": 636276111928.46,
        "_count": 213777
    },
    {
        "global__fiscalPeriod__28951.notation": "2016",
        "global__amount__0397f.sum": 12051686541.16,
        "global__amount__0397f__CZK.sum": 325672725401.77,
        "_count": 161797
    }
],
"order": [
    ["global__fiscalPeriod__28951.fiscalPeriod", "asc"]
],
"aggregates": ["", "_count"],
"summary": {
    "global__amount__0397f.sum": 945126777743.27,
    "global__amount__0397f__CZK.sum": 25485085887878
},
"attributes": [""]
}'

result = open_spending.ts(
  json_data =  sample.ts.data, 
  time ="global__fiscalPeriod__28951.notation",
  amount = "global__amount__0397f.sum"
  )
# Pretty output using prettify of jsonlite library
jsonlite::prettify(result,indent = 2)
## {
##   "acf.param": {
##     "acf.parameters": {
##       "acf": [
##         1,
##         0.6083,
##         0.1674,
##         -0.1663,
##         -0.1295,
##         -0.0727,
##         -0.0925,
##         -0.1301,
##         -0.1615,
##         -0.1959,
##         -0.2115,
##         -0.1311
##       ],
##       "acf.lag": [
##         0,
##         1,
##         2,
##         3,
##         4,
##         5,
##         6,
##         7,
##         8,
##         9,
##         10,
##         11
##       ],
##       "confidence.interval.up": [
##         0.5061
##       ],
##       "confidence.interval.low": [
##         -0.5061
##       ]
##     },
##     "pacf.parameters": {
##       "pacf": [
##         0.6083,
##         -0.3215,
##         -0.1865,
##         0.25,
##         -0.1593,
##         -0.1764,
##         0.0869,
##         -0.1346,
##         -0.2117,
##         -0.0036,
##         0.0508
##       ],
##       "pacf.lag": [
##         1,
##         2,
##         3,
##         4,
##         5,
##         6,
##         7,
##         8,
##         9,
##         10,
##         11
##       ],
##       "confidence.interval.up": [
##         0.5061
##       ],
##       "confidence.interval.low": [
##         -0.5061
##       ]
##     },
##     "acf.residuals.parameters": {
##       "acf.residuals": [
##         1,
##         0.3097,
##         0.2296,
##         -0.2346,
##         -0.0115,
##         -0.069,
##         -0.0524,
##         -0.0981,
##         -0.0842,
##         -0.1215,
##         -0.0934,
##         -0.0868,
##         -0.0484,
##         -0.2128,
##         -0.115,
##         -0.1051,
##         0.2946
##       ],
##       "acf.residuals.lag": [
##         0,
##         1,
##         2,
##         3,
##         4,
##         5,
##         6,
##         7,
##         8,
##         9,
##         10,
##         11,
##         12,
##         13,
##         14,
##         15,
##         16
##       ],
##       "confidence.interval.up": [
##         0.5061
##       ],
##       "confidence.interval.low": [
##         -0.5061
##       ]
##     },
##     "pacf.residuals.parameters": {
##       "pacf.residuals": [
##         0.3097,
##         0.1479,
##         -0.3857,
##         0.1673,
##         0.0455,
##         -0.2432,
##         0.0379,
##         0.0137,
##         -0.2159,
##         0.0048,
##         0.0175,
##         -0.1445,
##         -0.2757,
##         0.0882,
##         -0.0175,
##         0.2238
##       ],
##       "pacf.residuals.lag": [
##         1,
##         2,
##         3,
##         4,
##         5,
##         6,
##         7,
##         8,
##         9,
##         10,
##         11,
##         12,
##         13,
##         14,
##         15,
##         16
##       ],
##       "confidence.interval.up": [
##         0.5061
##       ],
##       "confidence.interval.low": [
##         -0.5061
##       ]
##     }
##   },
##   "decomposition": {
##     "stl.plot": {
##       "trend": [
##         -823419544.04,
##         1661560665.9804,
##         4624784833.2485,
##         7878983909.6147,
##         9164365784.5264,
##         1249040776.0474,
##         -4351015666.9835,
##         6551641382.3009,
##         57664029716.5692,
##         135646130024.628,
##         199114831577.553,
##         212547970266.68,
##         183231679540.212,
##         110152904453.676,
##         -12061960507.0426
##       ],
##       "conf.interval.up": [
##         100039247758.34,
##         66576136730.9101,
##         60840745923.6514,
##         68328241465.8754,
##         72409579665.7543,
##         65432105297.0944,
##         59676059487.2765,
##         70171989437.8921,
##         121691104870.829,
##         199829194545.675,
##         262360045458.781,
##         272997227822.941,
##         239447640630.614,
##         175067480518.606,
##         88800706795.3375
##       ],
##       "conf.interval.low": [
##         -101686086846.42,
##         -63253015398.9493,
##         -51591176257.1543,
##         -52570273646.646,
##         -54080848096.7016,
##         -62934023744.9996,
##         -68378090821.2435,
##         -57068706673.2904,
##         -6363045437.6908,
##         71463065503.5815,
##         135869617696.325,
##         152098712710.42,
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