I am new to time series analysis and related statistical tools. I am struggling with a time series for more than a week. I tried to check the Granger causality for the below data.
serdata <- read.csv("serdata.csv")
serdata
serdata$date = as.Date(serdata$date,format="%m/%d/%Y")
plot.ts(serdata)
## I could not interpret acf and pacf.
library(tseries)
acf(serdata$actual)
pacf(serdata$actual)
acf(serdata$digital)
pacf(serdata$digital)
adf.test(serdata$digital, alternative = "stationary")
Augmented Dickey-Fuller Test
data: serdata$digital
Dickey-Fuller = -2.1558, Lag order = 7, p-value = 0.5114
alternative hypothesis: stationary
kpss.test(serdata$digital)
KPSS Test for Level Stationarity
data: serdata$digital
KPSS Level = 5.5528, Truncation lag parameter = 4, p-value = 0.01
Warning message:
In kpss.test(serdata$digital) : p-value smaller than printed p-value
Box.test(serdata$digital, lag=20, type = "Ljung-Box")
Box-Ljung test
data: serdata$digital
X-squared = 4242.103, df = 20, p-value < 2.2e-16
## Grangertest gives very small p-value for both the series.
library(lmtest)
grangertest(serdata$digital~serdata$actual, order = 7, data = serdata)
grangertest(serdata$actual~serdata$digital, order = 7, data = serdata)
## Tried SMA
library("TTR")
SMAdigital<-SMA(serdata$digital,n=10)
plot.ts(SMAdigital)
SMAactual <-SMA(serdata$actual,n=10)
plot.ts(SMAactual)
grangertest(SMAdigital~SMAactual, order = 7, data = serdata)
grangertest(SMAactual~SMAdigital, order = 7, data = serdata)
I think the data is not stationary. Can some one help me to confirm ?
How can I remove the stationary ? I tried to use deompose() but got an error
Error in decompose(beonic$digital) :
time series has no or less than 2 periods
I am totally confused. Can someone guide me to check the causality ?
The data: serdata.csv
date actual digital
2/1/2016 5357 3205
2/2/2016 3717 4381
2/3/2016 3820 4379
2/4/2016 4566 4728
2/5/2016 4684 4494
2/6/2016 6563 4727
2/7/2016 6622 3606
2/8/2016 5734 3415
2/9/2016 4771 4373
2/10/2016 6107 4484
2/11/2016 4206 4448
2/12/2016 4845 4595
2/13/2016 6171 4464
2/14/2016 6883 3314
2/15/2016 4407 3565
2/16/2016 5271 3780
2/17/2016 6604 4312
2/18/2016 8226 4537
2/19/2016 9173 4350
2/20/2016 9143 4302
2/21/2016 8612 3343
2/22/2016 7252 3535
2/23/2016 5042 4245
2/24/2016 4832 4496
2/25/2016 5366 4456
2/26/2016 4916 4561
2/27/2016 7797 4519
2/28/2016 7760 3318
2/29/2016 4397 3393
3/1/2016 3845 4435
3/2/2016 4920 4537
3/3/2016 3976 4577
3/4/2016 5404 4661
3/5/2016 7341 4428
3/6/2016 5422 3358
3/7/2016 4488 3479
3/8/2016 3676 4400
3/9/2016 3968 4378
3/10/2016 4072 4609
3/11/2016 4311 4971
3/12/2016 6944 4755
3/13/2016 6394 3516
3/14/2016 3971 3678
3/15/2016 4308 4405
3/16/2016 3759 4386
3/17/2016 3652 4375
3/18/2016 4649 4472
3/19/2016 5979 4184
3/20/2016 5923 3375
3/21/2016 3822 3534
3/22/2016 2964 4325
3/23/2016 3505 4553
3/24/2016 4103 4344
3/25/2016 7998 4125
3/26/2016 8945 3351
3/27/2016 8162 2932
3/28/2016 6001 2828
3/29/2016 4277 3801
3/30/2016 3059 4020
3/31/2016 3243 4095
4/1/2016 4368 3884
4/2/2016 5335 3821
4/3/2016 5638 2984
4/4/2016 3586 3219
4/5/2016 2941 4085
4/6/2016 2731 4287
4/7/2016 3951 4425
4/8/2016 3460 4469
4/9/2016 6856 4086
4/10/2016 5136 3089
4/11/2016 3404 3200
4/12/2016 3033 4476
4/13/2016 3834 4165
4/14/2016 2886 4215
4/15/2016 3649 4008
4/16/2016 6266 3779
4/17/2016 5695 2898
4/18/2016 4740 2955
4/19/2016 4506 3872
4/20/2016 5324 4009
4/21/2016 4888 3971
4/22/2016 5555 4070
4/23/2016 7379 4066
4/24/2016 7688 2968
4/25/2016 5240 3083
4/26/2016 4672 4167
4/27/2016 4748 4258
4/28/2016 4779 4176
4/29/2016 4915 4288
4/30/2016 4936 4161
5/1/2016 5424 3155
5/2/2016 2240 3272
5/3/2016 2047 4296
5/4/2016 2411 4209
5/5/2016 2376 4242
5/6/2016 3058 4114
5/7/2016 4103 4071
5/8/2016 4229 2878
5/9/2016 2320 3039
5/10/2016 2292 4169
5/11/2016 2068 4419
5/12/2016 2443 4445
5/13/2016 2787 4769
5/14/2016 4595 4153
5/15/2016 4465 2912
5/16/2016 2082 3172
5/17/2016 2606 4235
5/18/2016 2547 4439
5/19/2016 2566 4433
5/20/2016 3321 4252
5/21/2016 5013 3776
5/22/2016 4883 3119
5/23/2016 2187 3157
5/24/2016 2705 4206
5/25/2016 2056 4407
5/26/2016 2193 4057
5/27/2016 2898 3941
5/28/2016 4744 3318
5/29/2016 4128 2814
5/30/2016 2537 3143
5/31/2016 1967 3099
6/1/2016 1903 3525
6/2/2016 2280 3709
6/3/2016 3195 3387
6/4/2016 5902 2969
6/5/2016 6553 2364
6/6/2016 4364 2577
6/7/2016 2171 3477
6/8/2016 2052 3578
6/9/2016 2274 3458
6/10/2016 2764 3432
6/11/2016 4334 3012
6/12/2016 4515 2723
6/13/2016 2244 3647
6/14/2016 1764 3127
6/15/2016 2287 3135
6/16/2016 2620 3154
6/17/2016 3539 3091
6/18/2016 6140 2496
6/19/2016 6020 2367
6/20/2016 2460 2975
6/21/2016 2019 3452
6/22/2016 2260 3153
6/23/2016 2357 2982
6/24/2016 3011 2786
6/25/2016 6115 2374
6/26/2016 5390 2412
6/27/2016 2294 2917
6/28/2016 2574 3117
6/29/2016 2210 3001
6/30/2016 2160 2826
7/1/2016 3164 2584
7/2/2016 4505 2256
7/3/2016 4611 2308
7/4/2016 4361 2427
7/5/2016 2433 2345
7/6/2016 2635 2577
7/7/2016 3293 2606
7/8/2016 2839 2602
7/9/2016 4455 2129
7/10/2016 5092 2081
7/11/2016 4109 2364
7/12/2016 4833 2408
7/13/2016 4955 2393
7/14/2016 5345 2416
7/15/2016 5266 2233
7/16/2016 7403 2049
7/17/2016 5792 2051
7/18/2016 4967 2206
7/19/2016 4634 2463
7/20/2016 4625 2439
7/21/2016 5005 2544
7/22/2016 5223 2398
7/23/2016 5172 2147
7/24/2016 4606 2253
7/25/2016 2407 2434
7/26/2016 2212 2604
7/27/2016 2155 2533
7/28/2016 2528 2672
7/29/2016 3446 2515
7/30/2016 5657 2175
7/31/2016 5198 2126
8/1/2016 2706 2462
8/2/2016 2299 2476
8/3/2016 2062 2633
8/4/2016 2231 2730
8/5/2016 2862 2554
8/6/2016 4005 2313
8/7/2016 4731 2249
8/8/2016 2177 2571
8/9/2016 2182 2585
8/10/2016 2285 2643
8/11/2016 2627 2476
8/12/2016 2885 2483
8/13/2016 6288 2449
8/14/2016 7410 2212
8/15/2016 2380 2615
8/16/2016 1823 2622
8/17/2016 1863 2573
8/18/2016 7 2723
8/19/2016 23 2580
8/20/2016 4329 2403
8/21/2016 4205 2369
8/22/2016 2162 2474
8/23/2016 2190 2754
8/24/2016 2041 2793
8/25/2016 2513 2791
8/26/2016 4491 2730
8/27/2016 5282 2724
8/28/2016 4737 2348
8/29/2016 2097 2629
8/30/2016 2110 3038
8/31/2016 2071 2901
9/1/2016 2473 2822
9/2/2016 2586 2862
9/3/2016 3551 2774
9/4/2016 4104 2539
9/5/2016 2025 2730
9/6/2016 2516 2937
9/7/2016 1983 3272
9/8/2016 1804 3270
9/9/2016 2283 2979
9/10/2016 4049 2780
9/11/2016 3792 2488
9/12/2016 2221 2777
9/13/2016 2337 3147
9/14/2016 2258 3105
9/15/2016 2276 3394
9/16/2016 2425 3043
9/17/2016 4567 3092
9/18/2016 3639 2761
9/19/2016 2616 2819
9/20/2016 2384 3365
9/21/2016 2735 3308
9/22/2016 2938 3164
9/23/2016 3386 3246
9/24/2016 4897 3261
9/25/2016 5788 2411
9/26/2016 4349 2297
9/27/2016 4451 3178
9/28/2016 4889 3326
9/29/2016 5002 3167
9/30/2016 5452 3102
10/1/2016 6223 3097
10/2/2016 6593 2575
10/3/2016 4574 2786
10/4/2016 4285 3188
10/5/2016 5323 3358
10/6/2016 4689 3537
10/7/2016 5499 3326
10/8/2016 5852 3198
10/9/2016 4987 2494
10/10/2016 2680 2834
10/11/2016 3128 3337
10/12/2016 2189 3686
10/13/2016 2532 3600
10/14/2016 3296 3630
10/15/2016 5019 3397
10/16/2016 4222 2666
10/17/2016 2482 2913
10/18/2016 2742 3746
10/19/2016 2611 3832
10/20/2016 2248 3716
10/21/2016 3463 3621
10/22/2016 5030 3530
10/23/2016 6164 2730
10/24/2016 4192 2774
10/25/2016 2879 4035
10/26/2016 2333 4054
10/27/2016 2710 3611
10/28/2016 3568 3846
10/29/2016 5415 3542
10/30/2016 5974 2684
10/31/2016 2314 2928
11/1/2016 2334 3108
11/2/2016 3379 3721
11/3/2016 2846 3884
11/4/2016 3183 4103
11/5/2016 4865 3797
11/6/2016 4948 3025
11/7/2016 3159 2651
11/8/2016 2724 1987
11/9/2016 2866 1833
11/10/2016 3600 2054
11/11/2016 5198 1862
11/12/2016 5192 1461
11/13/2016 4482 1311
11/14/2016 0 1557
11/15/2016 3 2014
11/16/2016 3284 2148
11/17/2016 2938 2033
11/18/2016 3710 1874
11/19/2016 4293 1572
11/20/2016 4239 1315
11/21/2016 4086 1715
11/22/2016 3054 1898
11/23/2016 3194 1797
11/24/2016 3033 1688
11/25/2016 3927 1462
11/26/2016 4824 1184
11/27/2016 4685 1237
11/28/2016 3072 1620
11/29/2016 3139 1916
11/30/2016 4363 1949
12/1/2016 2780 1907
12/2/2016 4075 1733
12/3/2016 5207 1453
12/4/2016 5327 1243
12/5/2016 4223 1569
12/6/2016 3179 1752
12/7/2016 3329 1697
12/8/2016 3747 1887
12/9/2016 3534 1797
12/10/2016 4673 1613
12/11/2016 5205 1229
12/12/2016 3600 1442
12/13/2016 4541 1871
12/14/2016 3823 1852
12/15/2016 3770 2155
12/16/2016 4370 2574
12/17/2016 4478 1434
12/18/2016 5396 1253
12/19/2016 5140 1306
12/20/2016 4089 1301
12/21/2016 4231 1333
12/22/2016 5657 1226
12/23/2016 6215 1074
12/24/2016 4211 841
12/25/2016 0 814
12/26/2016 5503 1035
12/27/2016 9483 1773
12/28/2016 6956 2030
12/29/2016 8992 1204
12/30/2016 6062 1135
12/31/2016 6326 1068
1/1/2017 7463 1067
1/2/2017 8426 1288
1/3/2017 8084 1322
1/4/2017 7026 1463
1/5/2017 6295 1480
1/6/2017 7179 1529
1/7/2017 5745 1474
1/8/2017 5690 1322
1/9/2017 5761 1404
1/10/2017 6332 1453
1/11/2017 6240 1056
1/12/2017 6710 1623
1/13/2017 5698 1714
1/14/2017 6156 1558
1/15/2017 7415 1365
1/16/2017 5742 1386
1/17/2017 5779 1671
1/18/2017 5784 1770
1/19/2017 5331 1680
1/20/2017 5476 1579
1/21/2017 7710 1290
1/22/2017 7187 1233
1/23/2017 7676 1352
1/24/2017 4742 1671
1/25/2017 5153 1745
1/26/2017 4817 1832
1/27/2017 5976 2170
1/28/2017 6145 2610
1/29/2017 5764 2238
1/30/2017 5305 2138
1/31/2017 4760 1898
2/1/2017 4752 2318
2/2/2017 4527 2223
2/3/2017 5206 6291
2/4/2017 6209 2040
2/5/2017 5729 1890
2/6/2017 7056 2225
2/7/2017 4955 2428
2/8/2017 4185 2302
2/9/2017 4090 2082
2/10/2017 3881 1994
2/11/2017 5280 1657
2/12/2017 6471 1768
2/13/2017 5840 1956
2/14/2017 4530 2148
2/15/2017 3993 2159
2/16/2017 4453 2188
2/17/2017 5570 2048
2/18/2017 7479 1959
2/19/2017 5349 1736
2/20/2017 4098 2041
2/21/2017 5032 2100
2/22/2017 4256 2253
2/23/2017 6215 2162
2/24/2017 4480 2055
2/25/2017 5995 1899
2/26/2017 6412 1836
2/27/2017 5450 2012
2/28/2017 3935 2243
Best Answer
The first thing you need to determine is whether your data is a trend stationary or difference stationary process.
A trend stationary process is one whereby, if the trend was removed from your data, then you would be left with a stationary dataset.
However, this would not be the case in data that has a unit root present, i.e. one where the null hypothesis of non-stationarity according to the Dickey-Fuller test cannot be rejected.
As well as the adf.test, you should also run a KPSS test to determine whether your data is trend stationary or not, with your null hypothesis being a trend stationary series, and the alternative being the presence of a unit root.
While we would need to see the acf and pacf plots to provide more clarity, in a non-stationary process you would expect to see a small decay in acf for each lag, whereas in a stationary process the same would drop sharply after the first lag.
You need to determine this since decomposing your data series and attempting to remove a trend would be incorrect if your data in fact is difference stationary, in which case differencing the series would be expected to transform your series into a stationary one.