Fish License Forecast
Jon Duan
2016-07-21
ARIMA Model
Load data in R
setwd("H:/Dropbox/Research/fish")
suppressMessages(library(vars))
suppressMessages(library(fpp))
suppressMessages(library(readxl))
suppressMessages(library(ggfortify))
mydata <- read.csv("fishData.csv", stringsAsFactors = F)
mydata$X_date_ <- as.Date(mydata$X_date_, "%Y-%m-%d")
mydata <- read.zoo(mydata, format = "%Y-%m-%d")
autoplot(scale(mydata))## Warning: Removed 12 rows containing missing values (geom_path).
Transform for vars
fish <- ts(mydata$sales, frequency = 12, start = c(2007,4),end = c(2016,3))
str(fish)## Time-Series [1:108] from 2007 to 2016: 16555 21567 17864 14217 9527 ...
## - attr(*, "index")= Date[1:108], format: "2007-04-01" "2007-05-01" ...head(fish)## [1] 16555 21567 17864 14217 9527 4235autoplot(fish) + ggtitle("Fish license")
Model selection
mod <- auto.arima(fish)
summary(mod)## Series: fish
## ARIMA(1,1,0)(2,1,1)[12]
##
## Coefficients:## Warning in sqrt(diag(x$var.coef)): 产生了NaNs## ar1 sar1 sar2 sma1
## -0.0297 -0.0703 0.0498 -0.6875
## s.e. 0.0056 0.0027 NaN 0.1308
##
## sigma^2 estimated as 6.01e+08: log likelihood=-1097.1
## AIC=2204.19 AICc=2204.87 BIC=2216.96
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -4177.506 22504.01 13407.13 -18.34982 27.6396 0.6298291
## ACF1
## Training set -0.0126558EViews code
sales.arimasel
equation eqR01.ls d(d(sales), 0,12) c sma(12)Compare to EViews’ best model
#library(fpp)
modEviews <- arima(fish, order=c(1,0,3), seasonal = list(order=c(1,1,1), periods=12))
summary(modEviews)##
## Call:
## arima(x = fish, order = c(1, 0, 3), seasonal = list(order = c(1, 1, 1), periods = 12))
##
## Coefficients:
## ar1 ma1 ma2 ma3 sar1 sma1
## 0.9763 -0.0159 0.0966 -0.0194 -0.1346 -0.6258
## s.e. 0.0401 0.1132 0.1055 0.1229 0.2188 0.2007
##
## sigma^2 estimated as 568578767: log likelihood = -1108.76, aic = 2231.52
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 55.90747 22481.18 13840.6 12.7412 35.28086 0.288061
## ACF1
## Training set 0.03631357EViews code
sales.arimasel
equation eqEViews01.ls sales c ar(1) ma(3) sar(12) sma(12)Forecast for next year/12 months for model 1
fcstR <- forecast(mod, h=12)
autoplot(fcstR)## Warning: `rbind_list()` is deprecated. Please use `bind_rows()` instead.
Forecast for next year/12 months for model 1
summary(fcstR)##
## Forecast method: ARIMA(1,1,0)(2,1,1)[12]
##
## Model Information:
## Series: fish
## ARIMA(1,1,0)(2,1,1)[12]
##
## Coefficients:## Warning in sqrt(diag(x$var.coef)): 产生了NaNs## ar1 sar1 sar2 sma1
## -0.0297 -0.0703 0.0498 -0.6875
## s.e. 0.0056 0.0027 NaN 0.1308
##
## sigma^2 estimated as 6.01e+08: log likelihood=-1097.1
## AIC=2204.19 AICc=2204.87 BIC=2216.96
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -4177.506 22504.01 13407.13 -18.34982 27.6396 0.6298291
## ACF1
## Training set -0.0126558
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Apr 2016 292655.54 261217.44 324093.6 244575.11 340736.0
## May 2016 338606.10 294805.88 382406.3 271619.44 405592.8
## Jun 2016 268469.57 215082.93 321856.2 186821.75 350117.4
## Jul 2016 230190.10 168694.05 291686.1 136140.01 324240.2
## Aug 2016 178715.69 110061.51 247369.9 73718.19 283713.2
## Sep 2016 88448.57 13315.17 163582.0 -26458.05 203355.2
## Oct 2016 53237.71 -27858.90 134334.3 -70788.86 177264.3
## Nov 2016 31158.23 -55492.17 117808.6 -101362.12 163678.6
## Dec 2016 31750.13 -60118.93 123619.2 -108751.47 172251.7
## Jan 2017 30438.00 -66368.80 127244.8 -117615.22 178491.2
## Feb 2017 26558.25 -74946.36 128062.9 -128679.66 181796.2
## Mar 2017 71404.65 -34589.80 177399.1 -90699.87 233509.2EViews code
freeze(rFcst) eqR01.forecast(e, g) salesfr01
Forecast for next year/12 months for model 2
fcstEViews <- forecast(modEviews, h=12)
autoplot(fcstEViews)## Warning: `rbind_list()` is deprecated. Please use `bind_rows()` instead.
Forecast for next year/12 months for model 2
summary(fcstEViews)##
## Forecast method: ARIMA(1,0,3)(1,1,1)[12]
##
## Model Information:
##
## Call:
## arima(x = fish, order = c(1, 0, 3), seasonal = list(order = c(1, 1, 1), periods = 12))
##
## Coefficients:
## ar1 ma1 ma2 ma3 sar1 sma1
## 0.9763 -0.0159 0.0966 -0.0194 -0.1346 -0.6258
## s.e. 0.0401 0.1132 0.1055 0.1229 0.2188 0.2007
##
## sigma^2 estimated as 568578767: log likelihood = -1108.76, aic = 2231.52
##
## Error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 55.90747 22481.18 13840.6 12.7412 35.28086 0.6501927
## ACF1
## Training set 0.03631357
##
## Forecasts:
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Apr 2016 291298.49 260734.23 321862.8 244554.49 338042.5
## May 2016 339578.85 297203.77 381953.9 274771.75 404386.0
## Jun 2016 267706.28 214842.59 320570.0 186858.25 348554.3
## Jul 2016 227771.93 166858.94 288684.9 134613.55 320930.3
## Aug 2016 175861.03 108160.88 243561.2 72322.59 279399.5
## Sep 2016 83891.90 10302.97 157480.8 -28652.65 196436.4
## Oct 2016 47954.89 -30838.29 126748.1 -72548.88 168458.7
## Nov 2016 24971.92 -58480.11 108423.9 -102656.95 152600.8
## Dec 2016 24930.83 -62731.57 112593.2 -109137.24 158998.9
## Jan 2017 22970.83 -68524.45 114466.1 -116959.13 162900.8
## Feb 2017 18437.18 -76567.53 113441.9 -126859.98 163734.3
## Mar 2017 62491.59 -35741.37 160724.6 -87742.76 212725.9EViews code
freeze(eviewsFcst) eqEViews01.forecast(e, g) salesfeviews01
VAR advantage and shortcoming
Vector autoregressions[https://www.otexts.org/fpp/9/2]
- Information criteria are commonly used to select the number of lags to be included.
- They are not built on some economic theory that imposes a theoretical structure to the equations. Every variable is assumed to influence every other variable in the system, which makes direct interpretation of the estimated coefficients very difficult.
VARs are useful in several contexts:
- forecasting a collection of related variables where no explicit interpretation is required;
- testing whether one variable is useful in forecasting another (the basis of Granger causality tests);
- impulse response analysis, where the response of one variable to a sudden but temporary change in another variable is analysed;
- forecast error variance decomposition, where the proportion of the forecast variance of one variable is attributed to the effect of other variables.
http://www.eviews.com/help/helpintro.html#page/content/VAR-Vector_Error_Correction_(VEC)_Models.html
Model selection
library(vars)
mydata <- ts(mydata, frequency = 12, start = c(2007,4),end = c(2016,3))
VARselect(mydata, lag.max=18, type="const")$selection## Warning in log(sigma.det): 产生了NaNs
## Warning in log(sigma.det): 产生了NaNs
## Warning in log(sigma.det): 产生了NaNs## AIC(n) HQ(n) SC(n) FPE(n)
## 18 18 18 17Model selection in EViews
smpl 2007m04 2015m03
var fishVARs.ls 1 12 gas_reg gdp income sales unempl
'test how many lag included
fishvars.laglen(12)
'Test cointegration/ Error correction
'http://www.eviews.com/help/helpintro.html#page/content/VAR-Vector_Error_Correction_(VEC)_Models.html
'test cointegration
fishvars.coint(c)
'change sample for esimation
smpl 2007m04 2015m03
fishvars.ec(c,4) 1 12 gas_reg gdp income sales unempl
'test lag numbers
fishvars.testlags
' Forecast
smpl 2015m04 2016m03
freeze(mode=overwrite, fcstVARs) fishvars.forecast(g, e) f
smpl 2014m04 2016m03
group gr02 sales salesfeviews01 salesfr01 sales_f
freeze(mode=overwrite, fcstCom) gr02.line
''model (1,0,3)(12,0, 12)12 is the best.
VECM Model
#install.packages("tsDyn")
library(tsDyn)
#Fit a VECM with Engle-Granger 2OLS estimator:
vecm.eg<-VECM(mydata, lag=12)
summary(vecm.eg) ## #############
## ###Model VECM
## #############
## Full sample size: 108 End sample size: 95
## Number of variables: 5 Number of estimated slope parameters 310
## AIC 4564.038 BIC 5365.956 SSR 41155676324
## Cointegrating vector (estimated by 2OLS):
## gas_reg gdp income sales unempl
## r1 1 -3.580473e-05 0.02553383 -5.645018e-05 0.5368104
##
##
## ECT Intercept
## Equation gas_reg -0.1951(0.1538) -2.5898(1.8156)
## Equation gdp 534.9695(746.1698) 1316.7612(8806.7975)
## Equation income 0.1601(0.6841) 17.8943(8.0741)*
## Equation sales 281.0379(813.0350) 10713.8131(9595.9847)
## Equation unempl 0.0032(0.0080) 0.3133(0.0939)**
## gas_reg -1 gdp -1
## Equation gas_reg 0.3637(0.1928). -1.7e-05(3.7e-05)
## Equation gdp 2395.2687(935.1757)* -0.0599(0.1791)
## Equation income -1.1685(0.8574) 0.0003(0.0002).
## Equation sales 255.7983(1018.9778) -0.2432(0.1951)
## Equation unempl 0.0009(0.0100) -1.3e-06(1.9e-06)
## income -1 sales -1
## Equation gas_reg -0.0154(0.0306) 3.5e-05(2.8e-05)
## Equation gdp -162.1497(148.2421) -0.1817(0.1369)
## Equation income -0.0493(0.1359) 9.5e-05(0.0001)
## Equation sales -438.7106(161.5263)* -0.3191(0.1491)*
## Equation unempl 0.0018(0.0016) -1.1e-06(1.5e-06)
## unempl -1 gas_reg -2
## Equation gas_reg -2.3434(2.5314) -0.1867(0.2213)
## Equation gdp -11421.5309(12278.9850) -305.1803(1073.3290)
## Equation income 1.1695(11.2574) -1.9122(0.9840).
## Equation sales -6379.9815(13379.3189) 1074.0722(1169.5112)
## Equation unempl -0.0885(0.1309) 0.0028(0.0114)
## gdp -2 income -2
## Equation gas_reg 2.4e-05(3.5e-05) 0.0719(0.0345)*
## Equation gdp -0.3168(0.1691). 4.0585(167.1518)
## Equation income -0.0002(0.0002) 0.1707(0.1532)
## Equation sales 0.2707(0.1842) -301.4060(182.1304)
## Equation unempl 9.9e-07(1.8e-06) -0.0018(0.0018)
## sales -2 unempl -2
## Equation gas_reg 7.7e-05(3.1e-05)* 0.1341(2.4448)
## Equation gdp 0.0351(0.1493) -15341.0419(11858.8221)
## Equation income 1.7e-05(0.0001) -12.9654(10.8722)
## Equation sales -0.3170(0.1626). 14856.2702(12921.5047)
## Equation unempl -1.4e-06(1.6e-06) -0.0104(0.1264)
## gas_reg -3 gdp -3
## Equation gas_reg 0.0598(0.2105) -2.1e-05(3.4e-05)
## Equation gdp 2414.2917(1020.8216)* 0.1159(0.1660)
## Equation income 1.2256(0.9359) 7.2e-05(0.0002)
## Equation sales -2525.5176(1112.2986)* -0.0130(0.1809)
## Equation unempl -0.0107(0.0109) -3.6e-06(1.8e-06).
## income -3 sales -3
## Equation gas_reg -0.0066(0.0354) 1.1e-05(3.3e-05)
## Equation gdp -105.7886(171.6227) -0.1589(0.1584)
## Equation income 0.0275(0.1573) -9.3e-05(0.0001)
## Equation sales 38.7596(187.0020) -0.2586(0.1726)
## Equation unempl -0.0003(0.0018) -1.2e-06(1.7e-06)
## unempl -3 gas_reg -4
## Equation gas_reg 1.0650(2.4732) 0.0656(0.2181)
## Equation gdp -2918.0809(11996.6764) -1430.6607(1057.8428)
## Equation income -0.9641(10.9986) 0.5912(0.9698)
## Equation sales -11182.3554(13071.7123) 390.2864(1152.6373)
## Equation unempl -0.5095(0.1279)*** -0.0023(0.0113)
## gdp -4 income -4
## Equation gas_reg 2.2e-05(3.5e-05) 0.0191(0.0347)
## Equation gdp 0.1420(0.1721) 86.0010(168.2666)
## Equation income -0.0003(0.0002). -0.2223(0.1543)
## Equation sales 0.0960(0.1875) 16.4749(183.3452)
## Equation unempl 2.1e-06(1.8e-06) 0.0002(0.0018)
## sales -4 unempl -4
## Equation gas_reg 1.3e-05(3.3e-05) -1.8883(2.6358)
## Equation gdp -0.0812(0.1600) -4498.0246(12785.1078)
## Equation income -0.0002(0.0001) 16.1799(11.7215)
## Equation sales -0.3404(0.1743). -17323.8614(13930.7959)
## Equation unempl -3.0e-06(1.7e-06). -0.0991(0.1363)
## gas_reg -5 gdp -5
## Equation gas_reg 0.0485(0.2157) 2.6e-05(3.2e-05)
## Equation gdp 1666.7760(1046.1195) -0.1546(0.1538)
## Equation income -0.4410(0.9591) -1.8e-05(0.0001)
## Equation sales -1293.7078(1139.8635) 0.1013(0.1676)
## Equation unempl 0.0213(0.0112). -4.8e-06(1.6e-06)**
## income -5 sales -5
## Equation gas_reg -0.0326(0.0334) 2.7e-05(3.4e-05)
## Equation gdp -289.9709(162.0881). -0.3138(0.1644).
## Equation income -0.2646(0.1486). -0.0003(0.0002).
## Equation sales 75.9873(176.6130) -0.2494(0.1791)
## Equation unempl -0.0028(0.0017) -2.8e-06(1.8e-06)
## unempl -5 gas_reg -6
## Equation gas_reg 0.7906(2.6825) -0.1943(0.2218)
## Equation gdp 14102.0058(13011.8589) -1459.3551(1075.9152)
## Equation income -7.8154(11.9294) -1.4136(0.9864)
## Equation sales 9512.6963(14177.8664) -70.6408(1172.3292)
## Equation unempl -0.1325(0.1387) -0.0019(0.0115)
## gdp -6 income -6
## Equation gas_reg 3.7e-05(3.1e-05) 0.0452(0.0306)
## Equation gdp 0.3316(0.1517)* 78.4726(148.2657)
## Equation income 0.0002(0.0001) -0.0340(0.1359)
## Equation sales 0.0067(0.1653) -60.7512(161.5520)
## Equation unempl -6.5e-07(1.6e-06) -0.0032(0.0016)*
## sales -6 unempl -6
## Equation gas_reg 4.7e-05(3.5e-05) -3.3694(2.7043)
## Equation gdp -0.0346(0.1678) 11550.7965(13117.3623)
## Equation income 3.9e-05(0.0002) -4.2471(12.0261)
## Equation sales -0.3482(0.1828). 20687.4666(14292.8241)
## Equation unempl -2.3e-06(1.8e-06) -0.0457(0.1399)
## gas_reg -7 gdp -7
## Equation gas_reg -0.2214(0.2132) 4.2e-07(3.3e-05)
## Equation gdp -1236.3713(1034.3020) 0.1296(0.1623)
## Equation income 0.6176(0.9483) -0.0001(0.0001)
## Equation sales -688.8040(1126.9870) 0.1149(0.1768)
## Equation unempl -0.0115(0.0110) -3.9e-07(1.7e-06)
## income -7 sales -7
## Equation gas_reg 0.0808(0.0293)** 5.2e-05(3.3e-05)
## Equation gdp -18.8246(142.1652) -0.1890(0.1585)
## Equation income 0.0214(0.1303) -0.0002(0.0001)
## Equation sales 89.7915(154.9048) -0.2326(0.1727)
## Equation unempl -0.0007(0.0015) -3.5e-06(1.7e-06)*
## unempl -7 gas_reg -8
## Equation gas_reg 1.2543(2.8529) -0.1025(0.2018)
## Equation gdp 32726.2672(13838.1205)* -104.3663(978.8209)
## Equation income -14.3431(12.6869) -0.7268(0.8974)
## Equation sales -2852.8343(15078.1702) 8.3954(1066.5341)
## Equation unempl -0.0950(0.1476) 0.0060(0.0104)
## gdp -8 income -8
## Equation gas_reg -9.5e-06(3.3e-05) 0.0342(0.0295)
## Equation gdp 0.4598(0.1612)** 280.7320(143.1597).
## Equation income -2.1e-05(0.0001) 0.1402(0.1312)
## Equation sales -0.2048(0.1757) -122.3082(155.9884)
## Equation unempl -2.3e-06(1.7e-06) -0.0010(0.0015)
## sales -8 unempl -8
## Equation gas_reg 1.7e-05(3.4e-05) 0.0886(2.9098)
## Equation gdp 0.0413(0.1641) 6806.5923(14114.4557)
## Equation income -4.2e-05(0.0002) -10.7449(12.9402)
## Equation sales -0.4514(0.1788)* 7959.8742(15379.2681)
## Equation unempl -1.5e-06(1.7e-06) -0.2741(0.1505).
## gas_reg -9 gdp -9
## Equation gas_reg 0.0208(0.1896) 3.8e-06(3.4e-05)
## Equation gdp -756.7692(919.7937) 0.2093(0.1652)
## Equation income 0.0604(0.8433) -0.0002(0.0002)
## Equation sales -1109.6027(1002.2175) 0.1259(0.1800)
## Equation unempl -0.0021(0.0098) 6.0e-07(1.8e-06)
## income -9 sales -9
## Equation gas_reg -0.0148(0.0315) 6.8e-05(3.5e-05).
## Equation gdp -20.3957(152.8635) -0.0339(0.1676)
## Equation income -0.1674(0.1401) 0.0002(0.0002)
## Equation sales 14.4365(166.5618) -0.1815(0.1826)
## Equation unempl -0.0003(0.0016) 4.6e-07(1.8e-06)
## unempl -9 gas_reg -10
## Equation gas_reg 2.7058(2.8117) -0.3485(0.1741).
## Equation gdp 21036.3629(13638.5958) -2474.7788(844.6149)**
## Equation income 7.6404(12.5039) 0.8794(0.7743)
## Equation sales -11998.7222(14860.7660) 634.0136(920.3018)
## Equation unempl -0.0755(0.1454) 0.0163(0.0090).
## gdp -10 income -10
## Equation gas_reg 4.2e-05(2.8e-05) -0.0015(0.0276)
## Equation gdp 0.2254(0.1371) 173.3305(134.0548)
## Equation income 0.0002(0.0001) -0.0193(0.1229)
## Equation sales -0.2140(0.1494) -47.4597(146.0676)
## Equation unempl -3.1e-06(1.5e-06)* -0.0003(0.0014)
## sales -10 unempl -10
## Equation gas_reg 4.8e-05(3.0e-05) 1.1114(2.8550)
## Equation gdp -0.0138(0.1479) 8637.2825(13848.2847)
## Equation income -0.0002(0.0001) 3.9099(12.6962)
## Equation sales -0.1215(0.1611) -3651.0894(15089.2453)
## Equation unempl -4.1e-06(1.6e-06)* 0.2701(0.1477).
## gas_reg -11 gdp -11
## Equation gas_reg 0.2508(0.1933) -3.6e-05(2.9e-05)
## Equation gdp 326.1566(937.8008) -0.2140(0.1387)
## Equation income -1.2618(0.8598) 0.0001(0.0001)
## Equation sales -662.5567(1021.8382) 0.1247(0.1512)
## Equation unempl -0.0135(0.0100) 2.4e-06(1.5e-06)
## income -11 sales -11
## Equation gas_reg 0.0025(0.0271) 4.0e-05(2.8e-05)
## Equation gdp -18.0584(131.4068) -0.0379(0.1355)
## Equation income -0.2598(0.1205)* -0.0001(0.0001)
## Equation sales 150.6045(143.1824) -0.2048(0.1477)
## Equation unempl -0.0021(0.0014) -8.1e-07(1.4e-06)
## unempl -11 gas_reg -12
## Equation gas_reg -0.1102(2.8333) -0.2573(0.1944)
## Equation gdp 34681.7501(13743.1325)* -1740.8921(943.0775).
## Equation income -4.3690(12.5998) -0.4689(0.8646)
## Equation sales -22147.1080(14974.6703) 651.4148(1027.5878)
## Equation unempl -0.0652(0.1465) -0.0027(0.0101)
## gdp -12 income -12
## Equation gas_reg 1.0e-05(2.9e-05) -0.0243(0.0259)
## Equation gdp 0.0234(0.1400) 12.6388(125.6020)
## Equation income 4.9e-05(0.0001) 0.2580(0.1152)*
## Equation sales -0.1426(0.1526) -250.5293(136.8573).
## Equation unempl -1.6e-07(1.5e-06) -0.0061(0.0013)***
## sales -12 unempl -12
## Equation gas_reg 5.5e-05(3.0e-05). -2.2712(2.6478)
## Equation gdp -0.1418(0.1465) 7988.3246(12843.6004)
## Equation income -0.0002(0.0001) -18.0133(11.7751)
## Equation sales 0.5600(0.1597)** -8513.8823(13994.5301)
## Equation unempl -4.5e-06(1.6e-06)** -0.1412(0.1369)#Fit a VECM with Johansen MLE estimator:
(vecm.jo<-VECM(mydata, lag=12, estim="ML")) ## ECT Intercept gas_reg -1 gdp -1
## Equation gas_reg -1.269930e-02 -1.932702e+01 1.937113e-01 -2.036379e-05
## Equation gdp 2.007470e+01 2.723294e+04 2.805846e+03 -5.685487e-02
## Equation income -1.646839e-02 -4.797690e+00 -1.130344e+00 3.023824e-04
## Equation sales -1.040000e+02 -1.308441e+05 3.991822e+01 -2.890912e-01
## Equation unempl 2.184861e-04 6.015808e-01 3.718874e-03 -1.246597e-06
## income -1 sales -1 unempl -1 gas_reg -2
## Equation gas_reg 7.074944e-03 1.968382e-04 -2.022548e+00 -3.316674e-01
## Equation gdp -1.840421e+02 -4.382655e-01 -1.257976e+04 8.418057e+01
## Equation income 4.866082e-03 3.046970e-04 3.987317e-01 -1.808003e+00
## Equation sales -1.407506e+02 1.008442e+00 -9.149967e+03 1.215855e+03
## Equation unempl 1.408104e-03 -3.907505e-06 -9.362102e-02 5.209538e-03
## gdp -2 income -2 sales -2 unempl -2
## Equation gas_reg 8.695587e-06 6.847954e-02 2.144087e-04 2.570963e-01
## Equation gdp -3.018542e-01 2.615415e+01 -1.800101e-01 -1.641171e+04
## Equation income -1.975682e-04 1.966752e-01 2.001234e-04 -1.440312e+01
## Equation sales 6.955750e-02 -1.913584e+02 8.303470e-01 8.599730e+03
## Equation unempl 1.261957e-06 -1.764517e-03 -3.800788e-06 -1.194618e-02
## gas_reg -3 gdp -3 income -3 sales -3
## Equation gas_reg 1.968561e-03 -9.000882e-06 -3.777545e-02 1.268402e-04
## Equation gdp 2.626511e+03 9.064273e-02 -3.608569e+01 -3.344027e-01
## Equation income 1.370607e+00 7.529130e-05 2.438559e-02 7.031690e-05
## Equation sales -1.998831e+03 2.985610e-02 -4.686892e+01 7.491686e-01
## Equation unempl -9.825635e-03 -3.753862e-06 2.657687e-04 -3.160160e-06
## unempl -3 gas_reg -4 gdp -4 income -4
## Equation gas_reg 2.5366917 -1.639486e-01 3.568290e-05 -3.391418e-03
## Equation gdp -6262.9297985 -9.382159e+02 1.063639e-01 1.400355e+02
## Equation income -0.9117946 5.295408e-01 -3.038406e-04 -2.177131e-01
## Equation sales -7571.3596060 -4.161958e+02 9.302676e-02 -1.418080e+01
## Equation unempl -0.5341512 1.520471e-03 1.876351e-06 6.038132e-04
## sales -4 unempl -4 gas_reg -5 gdp -5
## Equation gas_reg 1.153170e-04 -7.025498e-01 -1.707959e-01 4.358271e-05
## Equation gdp -2.354161e-01 -7.363252e+03 2.140747e+03 -1.873993e-01
## Equation income -4.989198e-06 1.591145e+01 -4.931118e-01 -5.164171e-06
## Equation sales 5.705800e-01 -1.582710e+04 -2.033320e+03 1.970713e-01
## Equation unempl -4.741629e-06 -1.188584e-01 2.502313e-02 -5.063117e-06
## income -5 sales -5 unempl -5 gas_reg -6
## Equation gas_reg -4.696301e-02 1.101267e-04 1.1236147 -5.075708e-01
## Equation gdp -2.480845e+02 -4.350472e-01 12438.7853681 -8.179680e+02
## Equation income -2.483334e-01 -1.327037e-04 -9.4557479 -1.553240e+00
## Equation sales 1.171026e+02 5.159638e-01 2816.2392968 -1.423608e+03
## Equation unempl -2.608432e-03 -4.240189e-06 -0.1374674 3.375103e-03
## gdp -6 income -6 sales -6 unempl -6
## Equation gas_reg 6.107241e-05 0.040890792 1.168022e-04 -2.131381e+00
## Equation gdp 2.824734e-01 96.238366203 -1.353454e-01 8.378159e+03
## Equation income 1.888533e-04 -0.019710564 1.469813e-04 -4.857215e+00
## Equation sales 1.119235e-01 -5.749282105 3.041298e-01 2.075067e+04
## Equation unempl -1.060456e-06 -0.003164324 -3.506677e-06 -6.619022e-02
## gas_reg -7 gdp -7 income -7 sales -7
## Equation gas_reg -4.493796e-01 1.773771e-05 0.0705944115 9.821960e-05
## Equation gdp -7.326068e+02 8.911339e-02 5.1717488924 -2.548808e-01
## Equation income 5.831627e-01 -1.206614e-04 0.0226602585 -1.493567e-04
## Equation sales -1.368222e+03 1.481432e-01 72.1594315981 1.996184e-01
## Equation unempl -7.663978e-03 -6.817731e-07 -0.0005322688 -4.311628e-06
## unempl -7 gas_reg -8 gdp -8 income -8
## Equation gas_reg 4.1215833 -3.619582e-01 2.000962e-05 3.222804e-02
## Equation gdp 26610.8716913 4.105157e+02 3.995971e-01 2.907285e+02
## Equation income -13.5099861 -8.722909e-01 -7.584500e-06 1.503083e-01
## Equation sales 7507.4810520 -1.247897e+03 -7.526673e-02 -8.082623e+01
## Equation unempl -0.1433432 1.042391e-02 -2.793411e-06 -9.990981e-04
## sales -8 unempl -8 gas_reg -9 gdp -9
## Equation gas_reg 5.199872e-05 2.6227405 -1.633424e-01 1.114185e-05
## Equation gdp -5.969816e-03 1408.4634056 -3.635833e+02 1.865488e-01
## Equation income 1.853822e-05 -9.9963974 7.863344e-03 -2.003253e-04
## Equation sales -9.317437e-02 17171.7595100 -1.770734e+03 9.326230e-02
## Equation unempl -2.075737e-06 -0.3167701 1.047068e-03 4.785957e-07
## income -9 sales -9 unempl -9 gas_reg -10
## Equation gas_reg -2.562016e-02 7.293961e-05 5.8073789 -5.528707e-01
## Equation gdp 4.098661e+00 -3.456524e-02 14617.5319657 -2.060023e+03
## Equation income -1.679316e-01 2.665432e-04 8.8992490 7.813552e-01
## Equation sales -1.258027e+01 -7.395514e-02 834.7093221 -2.802384e+02
## Equation unempl -1.625288e-04 3.638696e-07 -0.1278899 1.977733e-02
## gdp -10 income -10 sales -10 unempl -10
## Equation gas_reg 5.011097e-05 -7.916881e-03 2.829546e-05 3.4660691
## Equation gdp 2.065268e-01 1.952545e+02 2.848054e-02 3562.9183304
## Equation income 1.888199e-04 -6.378558e-03 -1.857010e-04 4.4986807
## Equation sales -1.875434e-01 -3.311188e+00 -2.007732e-01 4423.3243895
## Equation unempl -3.225174e-06 -2.212723e-04 -3.795343e-06 0.2304621
## gas_reg -11 gdp -11 income -11 sales -11
## Equation gas_reg 1.091411e-01 -4.639625e-05 -0.009223215 1.111145e-05
## Equation gdp 6.181629e+02 -2.016257e-01 9.884889949 1.567728e-02
## Equation income -1.321645e+00 7.901387e-05 -0.257898513 -1.508947e-04
## Equation sales -1.259392e+03 2.258552e-03 132.375021123 -3.648202e-01
## Equation unempl -1.107621e-02 2.545291e-06 -0.001892159 -3.241044e-07
## unempl -11 gas_reg -12 gdp -12 income -12
## Equation gas_reg 1.687013e+00 -4.069161e-01 6.368645e-07 -1.838793e-02
## Equation gdp 3.099925e+04 -1.421572e+03 3.683548e-02 1.114381e+01
## Equation income -3.572156e+00 -5.119165e-01 3.263149e-05 2.798570e-01
## Equation sales -1.440384e+04 1.130215e+02 -2.379695e-01 -1.378033e+02
## Equation unempl -9.561553e-02 -1.489632e-04 3.846647e-09 -6.188414e-03
## sales -12 unempl -12
## Equation gas_reg 1.600102e-05 -2.1055792
## Equation gdp -6.774621e-02 7463.1849757
## Equation income -2.017844e-04 -18.2786463
## Equation sales 3.448866e-01 -9341.3191231
## Equation unempl -3.791420e-06 -0.1438778fcstVEC <- predict(vecm.eg, n.ahead = 12)Forecast/predict of VECM
fcstVEC <- ts(fcstVEC, frequency = 12, start = c(2016,4),end = c(2017,3))
autoplot(fcstVEC[,'sales'])
ADL/ autoregression distribution lag model
Estimate in EViews tutorial
Selected Model: ARDL(12, 5, 2, 3, 7)
'ADL autoregression distribution model
'http://www.eviews.com/help/helpintro.html#page/content%2Fardl-Estimating_ARDL_Models_in_EViews.html%23
'Selected Model: ARDL(12, 5, 2, 3, 7)
smpl 2007m04 2015m03
equation eqardl.ardl(deplags=12, reglags=12, trend=linear) sales gas_reg gdp income unempl @
smpl 2015m04 2016m03
eqardl.forecast(e,g) salesfardl
freeze(mode=overwrite,fcstARDL) eqardl.forecast(e,g) salesfardl
smpl 2014m04 2016m03
group gr03 sales salesfeviews01 salesfr01 sales_f salesfardl
freeze(mode=overwrite, fcstCom) gr03.line
'''''''''''''''''''''''
'''conclusion
'arma model (1,0,3)(12,0, 12)12 is the best.
' ARDL(12, 5, 2, 3, 7) autoregression distribution model is the second.
'arima model (0,1,0)(0,1, 1)12 is the third.
'vecm model is the fourth, and it may need more tuning.Estimate ARDL in R tutorial
https://github.com/fcbarbi/ardl/blob/master/vignettes/ardl-vignette.Rmd
#install.packages("devtools")
#devtools::install_github("fcbarbi/ardl")
require(ardl)## Loading required package: ardlmydataZOO <- read.csv("fishData.csv", stringsAsFactors = F)
mydataZOO$X_date_ <- as.Date(mydataZOO$X_date_, "%Y-%m-%d")
mydataZOO <- head(mydataZOO, length(mydataZOO)-18)
mydataZOO <- read.zoo(mydataZOO, format = "%Y-%m-%d")
is.na(mydataZOO)## gas_reg gdp income sales unempl
## 1 FALSE FALSE FALSE FALSE FALSE
## 2 FALSE FALSE FALSE FALSE FALSE
## 3 FALSE FALSE FALSE FALSE FALSE
## 4 FALSE FALSE FALSE FALSE FALSE
## 5 FALSE FALSE FALSE FALSE FALSE
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## 104 FALSE FALSE FALSE FALSE FALSE
## 105 FALSE FALSE FALSE FALSE FALSE
## 106 FALSE FALSE FALSE FALSE FALSE
## 107 FALSE FALSE FALSE FALSE FALSE
## 108 FALSE FALSE FALSE FALSE FALSEmodARDL <- auto.ardl( sales~gas_reg+gdp+income+unempl, data=mydataZOO,
ymax=12, xmax=c(12,12,12,12), ic="bic" )
summary(modARDL)##
## Time series regression with "zoo" data:
## Start = 2008-04-01, End = 2016-03-01
##
## Call:
## dynlm::dynlm(formula = formula(fm), data = data, subset = subset)
##
## Residuals:
## Min 1Q Median 3Q Max
## -59937 -9561 -815 9209 62589
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 3.076e+05 9.726e+04 3.162 0.00226 **
## L(sales, 1) 6.933e-02 7.462e-02 0.929 0.35583
## L(sales, 2) -2.908e-01 6.989e-02 -4.161 8.35e-05 ***
## L(sales, 3) -2.358e-02 6.948e-02 -0.339 0.73525
## L(sales, 4) -2.157e-01 6.566e-02 -3.286 0.00155 **
## L(sales, 5) -1.703e-01 6.505e-02 -2.618 0.01070 *
## L(sales, 6) -1.522e-01 7.010e-02 -2.171 0.03312 *
## L(sales, 7) -1.806e-01 6.679e-02 -2.704 0.00847 **
## L(sales, 8) -1.292e-01 6.860e-02 -1.883 0.06359 .
## L(sales, 9) -1.094e-01 1.011e-01 -1.082 0.28270
## L(sales, 10) -1.021e-01 9.878e-02 -1.034 0.30446
## L(sales, 11) 7.050e-03 9.532e-02 0.074 0.94124
## L(sales, 12) 4.652e-01 7.476e-02 6.223 2.56e-08 ***
## gas_reg 4.015e+02 2.865e+02 1.402 0.16517
## gdp -3.438e-02 3.167e-02 -1.086 0.28114
## income -7.748e+01 9.672e+01 -0.801 0.42559
## L(income, 1) -1.647e+02 1.078e+02 -1.528 0.13082
## L(income, 2) -7.850e+01 1.038e+02 -0.756 0.45190
## L(income, 3) 3.468e+02 7.821e+01 4.434 3.11e-05 ***
## unempl 1.069e+04 7.800e+03 1.370 0.17465
## L(unempl, 1) -1.548e+04 7.091e+03 -2.183 0.03216 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 21010 on 75 degrees of freedom
## Multiple R-squared: 0.9739, Adjusted R-squared: 0.967
## F-statistic: 140 on 20 and 75 DF, p-value: < 2.2e-16ARDL(12, 1, 1, 3, 1)
Forecast by ARDL
In R, forecast need the new observation for other exogenous variables.
#fcstARDL <- forecast(modARDL, h=12)Forecast ARDL with auto.arima
fit_arima_dl=auto.arima(mydata[,"sales"], xreg= scale(mydata[,c('gas_reg', 'gdp', 'income','unempl')]) )
summary(fit_arima_dl)## Series: mydata[, "sales"]
## ARIMA(0,0,0)(1,0,1)[12] with non-zero mean
##
## Coefficients:
## sar1 sma1 intercept gas_reg gdp income unempl
## 0.8086 0.5676 86813.17 11701.60 25242.86 -40569.39 12893.785
## s.e. 0.0605 0.1982 25312.40 6156.54 15303.58 15342.38 6907.593
##
## sigma^2 estimated as 2.087e+09: log likelihood=-1321.65
## AIC=2659.29 AICc=2660.75 BIC=2680.75
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 7373.343 44179.05 28060.08 -215.2871 283.6685 1.318184
## ACF1
## Training set 0.6375803Forecast ARDL with auto.arima
#fcstAutoADL <- forecast(fit_arima_dl, h=12)