Univariate time series analysis for short and long time series data using the appropriate model.
ts.analysis(tsdata, x.order=NULL, prediction.steps=1, tojson=T)
| tsdata | The input univariate time series data |
|---|---|
| x.order | An integer vector of length 3 specifying the order of the Arima model |
| prediction.steps | The number of prediction steps |
| tojson | If TRUE the results are returned in json format, default returns a list |
A json string with the parameters:
acf.param
acf.parameters:
acf The estimated acf values of the input time series
acf.lag The lags at which the acf is estimated
confidence.interval.up The upper limit of the confidence interval
confidence.interval.low The lower limit of the confidence interval
pacf.parameters:
pacf The estimated pacf values of the input time series
pacf.lag The lags at which the pacf is estimated
confidence.interval.up The upper limit of the confidence interval
confidence.interval.low The lower limit of the confidence interval
acf.residuals.parameters:
acf.res The estimated acf values of the model residuals
acf.res.lag The lags at which the acf is estimated of the model residuals
confidence.interval.up The upper limit of the confidence interval
confidence.interval.low The lower limit of the confidence interval
pacf.residuals.parameters:
pacf.res The estimated pacf values of the model residuals
pacf.res.lag The lags at which the pacf is estimated of the model residuals
confidence.interval.up The upper limit of the confidence interval
confidence.interval.low The lower limit of the confidence interval
param
stl.plot:
trend The estimated trend component
trend.ci.up The estimated up limit for trend component (for non seasonal time series)
trend.ci.low The estimated low limit for trend component (for non seasonal time series)
seasonal The estimated seasonal component
remainder The estimated remainder component
time The time of the series was sampled
stl.general:
stl.degree The degree of fit
degfr The effective degrees of freedom for non seasonal time series
degfr.fitted The fitted degrees of freedom for non seasonal time series
fitted The model's fitted values
residuals The residuals of the model (fitted innovations)
compare:
arima.order The Arima order for seasonal time series
arima.coef A vector of AR, MA and regression coefficients
arima.coef.se The standard error of the coefficients
covariance.coef The matrix of the estimated variance of the coefficients
resid.variance The residuals variance
not.used.obs The number of not used observations for the fitting
used.obs The used observations for the fitting
loglik The maximized log-likelihood (of the differenced data), or the approximation to it used
aic The AIC value corresponding to the log-likelihood
bic The BIC value corresponding to the log-likelihood
gcv The generalized cross-validation statistic time series
aicc The second-order Akaike Information Criterion corresponding to the log-likelihood for seasonal time series
forecasts
ts.model a string indicating the arima orders
data_year The time that time series data were sampled
data The time series values
predict_time The time that defined by the prediction_steps parameter
predict_values The predicted values that defined by the prediction_steps parameter
up80 The upper limit of the 80% predicted confidence interval
low80 The lower limit of the 80% predicted confidence interval
up95 The upper limit of the 95% predicted confidence interval
low95 The lower limit of the 95% predicted confidence interval
This function automatically tests for stationarity of the input time series data using ts.stationary.test
function. Depending the nature of the time series data and the stationary tests there are four branches:
a.)short and non seasonal, b.)short and seasonal, c.)long and non seasonal and d.)long and seasonal.
For branches a and c ts.non.seas.model is used and for b and d ts.seasonal.model is used.
This function also decomposes both seasonal and non seasonal time series through ts.non.seas.decomp and
ts.seasonal.decomp and forecasts h steps ahead the user selected(default h=1) using ts.forecast.
ts.stationary.test, ts.acf, ts.seasonal.model, ts.seasonal.decomp,
ts.non.seas.model, ts.non.seas.decomp, ts.forecast
ts.analysis(Athens_draft_ts, prediction.steps=3)#> {"acf.param":{"acf.parameters":{"acf":[1,0.6701,0.2048,-0.2919,-0.5127,-0.5143,-0.282,-0.0182,0.1093,0.091,0.0325],"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":[0.6701,-0.4433,-0.4358,0.0271,-0.1179,0.0163,-0.0433,-0.2771,-0.1221,0.0503],"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":[1,0.843,0.7463,0.5848,0.4491,0.2929,0.1525,0.006,-0.1366,-0.2598,-0.3856,-0.4905,-0.6126,-0.5635,-0.522,-0.4455],"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":[0.843,0.1231,-0.2484,-0.0772,-0.1179,-0.0931,-0.1185,-0.1479,-0.0829,-0.1589,-0.1436,-0.2656,0.4077,0.159,-0.1307],"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":[698958230.0959,656722462.4698,666934797.6034,720359312.9533,825103477.7027,927286963.4796,955162556.072,901594076.3243,826636813.9483,777095660.2212,749465108.9076,753417720.7148],"conf.interval.up":[799474104.4628,718316873.2136,728193402.4122,787153597.0524,894791906.2167,998843432.4668,1026719025.0592,971282504.8383,893431098.0473,838354265.03,811059519.6515,853933595.0817],"conf.interval.low":[598442355.729,595128051.7259,605676192.7946,653565028.8543,755415049.1887,855730494.4925,883606087.0849,831905647.8104,759842529.8492,715837055.4123,687870698.1638,652901846.3479],"seasonal":{},"remainder":[21936769.9041,-27785462.4698,-48384797.6034,4470687.0467,33838522.2973,-7778963.4796,22325443.928,30012923.6757,39880579.0517,-109987660.2212,23957446.0924,6141563.2852],"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":[21936769.9041,-27785462.4698,-48384797.6034,4470687.0467,33838522.2973,-7778963.4796,22325443.928,30012923.6757,39880579.0517,-109987660.2212,23957446.0924,6141563.2852],"fitted":[698958230.0959,656722462.4698,666934797.6034,720359312.9533,825103477.7027,927286963.4796,955162556.072,901594076.3243,826636813.9483,777095660.2212,749465108.9076,753417720.7148],"time":[2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015],"line":[0]},"compare":{"resid.variance":[1.86531930797979e+015],"used.obs":[2004,2015,2009.5,2006.75,2012.25],"loglik":[-1.02592561938889e+016],"aic":[2.05185123877777e+016],"bic":[2.05185123877777e+016],"gcv":[5.68320742803746e+015]}},"model.param":{"model":{"arima.order":[1,1,0,0,1,1,0],"arima.coef":[0.1441,0.0153],"arima.coef.se":[0.8665,0.8392]},"residuals_fitted":{"residuals":[720894.6302,-90787238.6325,4239112.9372,107712202.5897,117144839.4241,39442974.6622,48646734.4435,-54982432.2565,-57635036.0029,-189145649.1128,137951183.7204,-31298309.7508],"fitted":[720174105.3698,719724238.6325,614310887.0628,617117797.4103,741797160.5759,880065025.3378,928841265.5565,986589432.2565,924152429.0029,856253649.1128,635471371.2796,790857593.7508],"time":[2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015],"line":[0]},"compare":{"resid.variance":[1.10709947302236e+016],"variance.coef":[[0.7508,-0.6832],[-0.6832,0.7043]],"not.used.obs":[0],"used.obs":[11],"loglik":[-217.7045],"aic":[441.409],"bic":[442.6027],"aicc":[444.8376]}},"forecasts":{"ts.model":["ARIMA(1,1,1)"],"data_year":[2004,2005,2006,2007,2008,2009,2010,2011,2012,2013,2014,2015],"data":[720895000,628937000,618550000,724830000,858942000,919508000,977488000,931607000,866517393,667108000,773422555,759559284],"predict_time":[2016,2017,2018],"predict_values":[757082034.9521,756724985.1315,756673522.9766],"up80":[891925345.8547,963185026.4698,1017532317.1036],"low80":[622238724.0495,550264943.7933,495814728.8496],"up95":[963307082.801,1072478370.4413,1155622621.3081],"low95":[550856987.1032,440971599.8218,357724424.6451]}}