::Free Statistics and Forecasting Software::

All rights reserved. The non-commercial (academic) use of this software is free of charge. The only thing that is asked in return is to cite this software when results are used in publications.

This free online software (calculator) computes the bivariate Granger causality test in two directions. Enter the time series in the respective data boxes and specify the Box-Cox tranformation parameter, the degree of non-seasonal differencing, and the degree of seasonal differencing (for each time series) to induce stationarity. The maximum number lags (of the endogenous variable) that is used in the test equation can also be specified.

Enter (or paste) your data delimited by hard returns.

Send output to:
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Data X (click to load default data)
87.28 87.28 87.09 86.92 87.59 90.72 90.69 90.3 89.55 88.94 88.41 87.82 87.07 86.82 86.4 86.02 85.66 85.32 85 84.67 83.94 82.83 81.95 81.19 80.48 78.86 69.47 68.77 70.06 73.95 75.8 77.79 81.57 83.07 84.34 85.1 85.25 84.26 83.63 86.44 85.3 84.1 83.36 82.48 81.58 80.47 79.34 82.13 81.69 80.7 79.88 79.16 78.38 77.42 76.47 75.46 74.48 78.27 80.7 79.91 78.75 77.78 81.14 81.08 80.03 78.91 78.01 76.9 75.97 81.93 80.27 78.67 77.42 76.16 74.7 76.39 76.04 74.65 73.29 71.79 74.39 74.91 74.54 73.08 72.75 71.32 70.38 70.35 70.01 69.36 67.77 69.26 69.8 68.38 67.62 68.39 66.95 65.21 66.64 63.45 60.66 62.34 60.32 58.64 60.46 58.59 61.87 61.85 67.44 77.06 91.74 93.15 94.15 93.11 91.51 89.96 88.16 86.98 88.03 86.24 84.65 83.23 81.7 80.25 78.8 77.51 76.2 75.04 74 75.49 77.14 76.15 76.27 78.19 76.49 77.31 76.65 74.99 73.51 72.07 70.59 71.96 76.29 74.86 74.93 71.9 71.01 77.47 75.78 76.6 76.07 74.57 73.02 72.65 73.16 71.53 69.78 67.98 69.96 72.16 70.47 68.86 67.37 65.87 72.16 71.34 69.93 68.44 67.16 66.01 67.25 70.91 69.75 68.59 67.48 66.31 64.81 66.58 65.97 64.7 64.7 60.94 59.08 58.42 57.77 57.11 53.31 49.96 49.4 48.84 48.3 47.74 47.24 46.76 46.29 48.9 49.23 48.53 48.03 54.34 53.79 53.24 52.96 52.17 51.7 58.55 78.2 77.03 76.19 77.15 75.87 95.47 109.67 112.28 112.01 107.93 105.96 105.06 102.98 102.2 105.23 101.85 99.89 96.23 94.76 91.51 91.63 91.54 85.23 87.83 87.38 84.44 85.19 84.03 86.73 102.52 104.45 106.98 107.02 99.26 94.45 113.44 157.33 147.38 171.89 171.95 132.71 126.02 121.18 115.45 110.48 117.85 117.63 124.65 109.59 111.27 99.78 98.21 99.2 97.97 89.55 87.91 93.34 94.42 93.2 90.29 91.46 89.98 88.35 88.41 82.44 79.89 75.69 75.66 84.5 96.73 87.48 82.39 83.48 79.31 78.16 72.77 72.45 68.46 67.62 68.76 70.07 68.55 65.3 58.96 59.17 62.37 66.28 55.62 55.23 55.85 56.75 50.89 53.88 52.95 55.08 53.61 58.78 61.85 55.91 53.32 46.41 44.57 50 50 53.36 46.23 50.45 49.07 45.85 48.45 49.96 46.53 50.51 47.58 48.05 46.84 47.67 49.16 55.54 55.82 58.22 56.19 57.77 63.19 54.76 55.74 62.54 61.39 69.6 79.23 80 93.68 107.63 100.18 97.3 90.45 80.64 80.58 75.82 85.59 89.35 89.42 104.73 95.32 89.27 90.44 86.97 79.98 81.22 87.35 83.64 82.22 94.4 102.18
Data Y:
255 280.2 299.9 339.2 374.2 393.5 389.2 381.7 375.2 369 357.4 352.1 346.5 342.9 340.3 328.3 322.9 314.3 308.9 294 285.6 281.2 280.3 278.8 274.5 270.4 263.4 259.9 258 262.7 284.7 311.3 322.1 327 331.3 333.3 321.4 327 320 314.7 316.7 314.4 321.3 318.2 307.2 301.3 287.5 277.7 274.4 258.8 253.3 251 248.4 249.5 246.1 244.5 243.6 244 240.8 249.8 248 259.4 260.5 260.8 261.3 259.5 256.6 257.9 256.5 254.2 253.3 253.8 255.5 257.1 257.3 253.2 252.8 252 250.7 252.2 250 251 253.4 251.2 255.6 261.1 258.9 259.9 261.2 264.7 267.1 266.4 267.7 268.6 267.5 268.5 268.5 270.5 270.9 270.1 269.3 269.8 270.1 264.9 263.7 264.8 263.7 255.9 276.2 360.1 380.5 373.7 369.8 366.6 359.3 345.8 326.2 324.5 328.1 327.5 324.4 316.5 310.9 301.5 291.7 290.4 287.4 277.7 281.6 288 276 272.9 283 283.3 276.8 284.5 282.7 281.2 287.4 283.1 284 285.5 289.2 292.5 296.4 305.2 303.9 311.5 316.3 316.7 322.5 317.1 309.8 303.8 290.3 293.7 291.7 296.5 289.1 288.5 293.8 297.7 305.4 302.7 302.5 303 294.5 294.1 294.5 297.1 289.4 292.4 287.9 286.6 280.5 272.4 269.2 270.6 267.3 262.5 266.8 268.8 263.1 261.2 266 262.5 265.2 261.3 253.7 249.2 239.1 236.4 235.2 245.2 246.2 247.7 251.4 253.3 254.8 250 249.3 241.5 243.3 248 253 252.9 251.5 251.6 253.5 259.8 334.1 448 445.8 445 448.2 438.2 439.8 423.4 410.8 408.4 406.7 405.9 402.7 405.1 399.6 386.5 381.4 375.2 357.7 359 355 352.7 344.4 343.8 338 339 333.3 334.4 328.3 330.7 330 331.6 351.2 389.4 410.9 442.8 462.8 466.9 461.7 439.2 430.3 416.1 402.5 397.3 403.3 395.9 387.8 378.6 377.1 370.4 362 350.3 348.2 344.6 343.5 342.8 347.6 346.6 349.5 342.1 342 342.8 339.3 348.2 333.7 334.7 354 367.7 363.3 358.4 353.1 343.1 344.6 344.4 333.9 331.7 324.3 321.2 322.4 321.7 320.5 312.8 309.7 315.6 309.7 304.6 302.5 301.5 298.8 291.3 293.6 294.6 285.9 297.6 301.1 293.8 297.7 292.9 292.1 287.2 288.2 283.8 299.9 292.4 293.3 300.8 293.7 293.1 294.4 292.1 291.9 282.5 277.9 287.5 289.2 285.6 293.2 290.8 283.1 275 287.8 287.8 287.4 284 277.8 277.6 304.9 294 300.9 324 332.9 341.6 333.4 348.2 344.7 344.7 329.3 323.5 323.2 317.4 330.1 329.2 334.9 315.8 315.4 319.6 317.3 313.8 315.8 311.3
Sample Range: (leave blank to include all observations)
From:
To:
Box-Cox transformation parameter (X series)
1-2.0-1.9-1.8-1.7-1.6-1.5-1.4-1.3-1.2-1.1-1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.0
Degree (d) of non-seasonal differencing (X series)
012
Degree (D) of seasonal differencing (X series)
012
Seasonal Period
123412
Box-Cox transformation parameter (Y series)
1-2.0-1.9-1.8-1.7-1.6-1.5-1.4-1.3-1.2-1.1-1.0-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.61.71.81.92.0
Degree (d) of non-seasonal differencing (Y series)
012
Degree (D) of seasonal differencing (Y series)
012
Number of non-seasonal time lags in test
1234567891011
Chart options
Width:
Height:

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Click here to edit the underlying code of this R Module.

Source code of R module

library(lmtest) par1 <- as.numeric(par1) par2 <- as.numeric(par2) par3 <- as.numeric(par3) par4 <- as.numeric(par4) par5 <- as.numeric(par5) par6 <- as.numeric(par6) par7 <- as.numeric(par7) par8 <- as.numeric(par8) ox <- x oy <- y if (par1 == 0) { x <- log(x) } else { x <- (x ^ par1 - 1) / par1 } if (par5 == 0) { y <- log(y) } else { y <- (y ^ par5 - 1) / par5 } if (par2 > 0) x <- diff(x,lag=1,difference=par2) if (par6 > 0) y <- diff(y,lag=1,difference=par6) if (par3 > 0) x <- diff(x,lag=par4,difference=par3) if (par7 > 0) y <- diff(y,lag=par4,difference=par7) x y (gyx <- grangertest(y ~ x, order=par8)) (gxy <- grangertest(x ~ y, order=par8)) bitmap(file="test1.png") op <- par(mfrow=c(2,1)) (r <- ccf(ox,oy,main="Cross Correlation Function (raw data)",ylab="CCF",xlab="Lag (k)")) (r <- ccf(x,y,main="Cross Correlation Function (transformed and differenced)",ylab="CCF",xlab="Lag (k)")) par(op) dev.off() bitmap(file="test2.png") op <- par(mfrow=c(2,1)) acf(ox,lag.max=round(length(x)/2),main="ACF of x (raw)") acf(x,lag.max=round(length(x)/2),main="ACF of x (transformed and differenced)") par(op) dev.off() bitmap(file="test3.png") op <- par(mfrow=c(2,1)) acf(oy,lag.max=round(length(y)/2),main="ACF of y (raw)") acf(y,lag.max=round(length(y)/2),main="ACF of y (transformed and differenced)") par(op) dev.off() load(file="createtable") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Granger Causality Test: Y = f(X)",5,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Model",header=TRUE) a<-table.element(a,"Res.DF",header=TRUE) a<-table.element(a,"Diff. DF",header=TRUE) a<-table.element(a,"F",header=TRUE) a<-table.element(a,"p-value",header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Complete model",header=TRUE) a<-table.element(a,gyx$Res.Df[1]) a<-table.element(a,"") a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Reduced model",header=TRUE) a<-table.element(a,gyx$Res.Df[2]) a<-table.element(a,gyx$Df[2]) a<-table.element(a,gyx$F[2]) a<-table.element(a,gyx$Pr[2]) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable1.tab") a<-table.start() a<-table.row.start(a) a<-table.element(a,"Granger Causality Test: X = f(Y)",5,TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Model",header=TRUE) a<-table.element(a,"Res.DF",header=TRUE) a<-table.element(a,"Diff. DF",header=TRUE) a<-table.element(a,"F",header=TRUE) a<-table.element(a,"p-value",header=TRUE) a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Complete model",header=TRUE) a<-table.element(a,gxy$Res.Df[1]) a<-table.element(a,"") a<-table.element(a,"") a<-table.element(a,"") a<-table.row.end(a) a<-table.row.start(a) a<-table.element(a,"Reduced model",header=TRUE) a<-table.element(a,gxy$Res.Df[2]) a<-table.element(a,gxy$Df[2]) a<-table.element(a,gxy$F[2]) a<-table.element(a,gxy$Pr[2]) a<-table.row.end(a) a<-table.end(a) table.save(a,file="mytable2.tab")

Cite this software as:

Wessa P., (2008), Bivariate Granger Causality (v1.0.0) in Free Statistics Software (v1.1.23-r7), Office for Research Development and Education, URL http://www.wessa.net/rwasp_grangercausality.wasp/

The R code is based on :

Anil K Seth (2007) Granger causality.Scholarpedia, 2(7):1667

To cite Wessa.net in publications use:
Wessa, P. (2012), Free Statistics Software, Office for Research Development and Education,
version 1.1.23-r7, URL http://www.wessa.net/

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Software Version : 1.1.23-r7
Algorithms & Software : Patrick Wessa, PhD
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