I am doing analysis to a dataset about U.S. Imports of Goods by Customs Basis from China.

I deleted the data of the first 5 years, logged the data, and then decomposed it (or HoltWinters, which also leads to this problem).

The random part passed my stationary test, so I fitted an ARIMA model and tested its residuals.

Weird thing happened: the larger my lag, the smaller my p-value.

Through spectral density plot and acf plot, I think it is not a long memory model. So... What's wrong with my model? How to improve it?

This is my code.

imp <- IMPCH$IMPCH[-c(1:60)]
length(imp)
imp.ts <- ts(imp, frequency = 12, start = 1990)
log.imp.ts <- log(imp.ts)
ts.plot(log.imp.ts)

log.imp.ts.de <- decompose(log.imp.ts)
#log.imp.ts.hw <- HoltWinters(log.imp.ts)
log.imp.ts.random <- log.imp.ts.de$random
#log.imp.ts.random <- resid(log.imp.ts.hw)


library(tseries)
adf.test(log.imp.ts.random)
pp.test(log.imp.ts.random)
kpss.test(log.imp.ts.random)

log.imp.ts.random = na.omit(log.imp.ts.random)
acf(log.imp.ts.random)
pacf(log.imp.ts.random)
spectrum(log.imp.ts.random)

library(forecast)
fit <- auto.arima(log.imp.ts.random, approximation = FALSE, stepwise = FALSE)
summary(fit)
tsdiag(fit)

# Ljung Box Test
Box.test(fit$residuals, type = "Ljung-Box")
Box.test(fit$residuals^2, type = "Ljung-Box")
Box.test(fit$residuals, lag = 24, type = "Ljung-Box")
Box.test(fit$residuals, lag = 36, type = "Ljung-Box")
log.imp.random.res <- fit$residuals
spectrum(log.imp.random.res)

This is the data I dput from R.

structure(list(DATE = structure(1:412, .Label = c("1985-01-01", 
"1985-02-01", "1985-03-01", "1985-04-01", "1985-05-01", "1985-06-01", 
"1985-07-01", "1985-08-01", "1985-09-01", "1985-10-01", "1985-11-01", 
"1985-12-01", "1986-01-01", "1986-02-01", "1986-03-01", "1986-04-01", 
"1986-05-01", "1986-06-01", "1986-07-01", "1986-08-01", "1986-09-01", 
"1986-10-01", "1986-11-01", "1986-12-01", "1987-01-01", "1987-02-01", 
"1987-03-01", "1987-04-01", "1987-05-01", "1987-06-01", "1987-07-01", 
"1987-08-01", "1987-09-01", "1987-10-01", "1987-11-01", "1987-12-01", 
"1988-01-01", "1988-02-01", "1988-03-01", "1988-04-01", "1988-05-01", 
"1988-06-01", "1988-07-01", "1988-08-01", "1988-09-01", "1988-10-01", 
"1988-11-01", "1988-12-01", "1989-01-01", "1989-02-01", "1989-03-01", 
"1989-04-01", "1989-05-01", "1989-06-01", "1989-07-01", "1989-08-01", 
"1989-09-01", "1989-10-01", "1989-11-01", "1989-12-01", "1990-01-01", 
"1990-02-01", "1990-03-01", "1990-04-01", "1990-05-01", "1990-06-01", 
"1990-07-01", "1990-08-01", "1990-09-01", "1990-10-01", "1990-11-01", 
"1990-12-01", "1991-01-01", "1991-02-01", "1991-03-01", "1991-04-01", 
"1991-05-01", "1991-06-01", "1991-07-01", "1991-08-01", "1991-09-01", 
"1991-10-01", "1991-11-01", "1991-12-01", "1992-01-01", "1992-02-01", 
"1992-03-01", "1992-04-01", "1992-05-01", "1992-06-01", "1992-07-01", 
"1992-08-01", "1992-09-01", "1992-10-01", "1992-11-01", "1992-12-01", 
"1993-01-01", "1993-02-01", "1993-03-01", "1993-04-01", "1993-05-01", 
"1993-06-01", "1993-07-01", "1993-08-01", "1993-09-01", "1993-10-01", 
"1993-11-01", "1993-12-01", "1994-01-01", "1994-02-01", "1994-03-01", 
"1994-04-01", "1994-05-01", "1994-06-01", "1994-07-01", "1994-08-01", 
"1994-09-01", "1994-10-01", "1994-11-01", "1994-12-01", "1995-01-01", 
"1995-02-01", "1995-03-01", "1995-04-01", "1995-05-01", "1995-06-01", 
"1995-07-01", "1995-08-01", "1995-09-01", "1995-10-01", "1995-11-01", 
"1995-12-01", "1996-01-01", "1996-02-01", "1996-03-01", "1996-04-01", 
"1996-05-01", "1996-06-01", "1996-07-01", "1996-08-01", "1996-09-01", 
"1996-10-01", "1996-11-01", "1996-12-01", "1997-01-01", "1997-02-01", 
"1997-03-01", "1997-04-01", "1997-05-01", "1997-06-01", "1997-07-01", 
"1997-08-01", "1997-09-01", "1997-10-01", "1997-11-01", "1997-12-01", 
"1998-01-01", "1998-02-01", "1998-03-01", "1998-04-01", "1998-05-01", 
"1998-06-01", "1998-07-01", "1998-08-01", "1998-09-01", "1998-10-01", 
"1998-11-01", "1998-12-01", "1999-01-01", "1999-02-01", "1999-03-01", 
"1999-04-01", "1999-05-01", "1999-06-01", "1999-07-01", "1999-08-01", 
"1999-09-01", "1999-10-01", "1999-11-01", "1999-12-01", "2000-01-01", 
"2000-02-01", "2000-03-01", "2000-04-01", "2000-05-01", "2000-06-01", 
"2000-07-01", "2000-08-01", "2000-09-01", "2000-10-01", "2000-11-01", 
"2000-12-01", "2001-01-01", "2001-02-01", "2001-03-01", "2001-04-01", 
"2001-05-01", "2001-06-01", "2001-07-01", "2001-08-01", "2001-09-01", 
"2001-10-01", "2001-11-01", "2001-12-01", "2002-01-01", "2002-02-01", 
"2002-03-01", "2002-04-01", "2002-05-01", "2002-06-01", "2002-07-01", 
"2002-08-01", "2002-09-01", "2002-10-01", "2002-11-01", "2002-12-01", 
"2003-01-01", "2003-02-01", "2003-03-01", "2003-04-01", "2003-05-01", 
"2003-06-01", "2003-07-01", "2003-08-01", "2003-09-01", "2003-10-01", 
"2003-11-01", "2003-12-01", "2004-01-01", "2004-02-01", "2004-03-01", 
"2004-04-01", "2004-05-01", "2004-06-01", "2004-07-01", "2004-08-01", 
"2004-09-01", "2004-10-01", "2004-11-01", "2004-12-01", "2005-01-01", 
"2005-02-01", "2005-03-01", "2005-04-01", "2005-05-01", "2005-06-01", 
"2005-07-01", "2005-08-01", "2005-09-01", "2005-10-01", "2005-11-01", 
"2005-12-01", "2006-01-01", "2006-02-01", "2006-03-01", "2006-04-01", 
"2006-05-01", "2006-06-01", "2006-07-01", "2006-08-01", "2006-09-01", 
"2006-10-01", "2006-11-01", "2006-12-01", "2007-01-01", "2007-02-01", 
"2007-03-01", "2007-04-01", "2007-05-01", "2007-06-01", "2007-07-01", 
"2007-08-01", "2007-09-01", "2007-10-01", "2007-11-01", "2007-12-01", 
"2008-01-01", "2008-02-01", "2008-03-01", "2008-04-01", "2008-05-01", 
"2008-06-01", "2008-07-01", "2008-08-01", "2008-09-01", "2008-10-01", 
"2008-11-01", "2008-12-01", "2009-01-01", "2009-02-01", "2009-03-01", 
"2009-04-01", "2009-05-01", "2009-06-01", "2009-07-01", "2009-08-01", 
"2009-09-01", "2009-10-01", "2009-11-01", "2009-12-01", "2010-01-01", 
"2010-02-01", "2010-03-01", "2010-04-01", "2010-05-01", "2010-06-01", 
"2010-07-01", "2010-08-01", "2010-09-01", "2010-10-01", "2010-11-01", 
"2010-12-01", "2011-01-01", "2011-02-01", "2011-03-01", "2011-04-01", 
"2011-05-01", "2011-06-01", "2011-07-01", "2011-08-01", "2011-09-01", 
"2011-10-01", "2011-11-01", "2011-12-01", "2012-01-01", "2012-02-01", 
"2012-03-01", "2012-04-01", "2012-05-01", "2012-06-01", "2012-07-01", 
"2012-08-01", "2012-09-01", "2012-10-01", "2012-11-01", "2012-12-01", 
"2013-01-01", "2013-02-01", "2013-03-01", "2013-04-01", "2013-05-01", 
"2013-06-01", "2013-07-01", "2013-08-01", "2013-09-01", "2013-10-01", 
"2013-11-01", "2013-12-01", "2014-01-01", "2014-02-01", "2014-03-01", 
"2014-04-01", "2014-05-01", "2014-06-01", "2014-07-01", "2014-08-01", 
"2014-09-01", "2014-10-01", "2014-11-01", "2014-12-01", "2015-01-01", 
"2015-02-01", "2015-03-01", "2015-04-01", "2015-05-01", "2015-06-01", 
"2015-07-01", "2015-08-01", "2015-09-01", "2015-10-01", "2015-11-01", 
"2015-12-01", "2016-01-01", "2016-02-01", "2016-03-01", "2016-04-01", 
"2016-05-01", "2016-06-01", "2016-07-01", "2016-08-01", "2016-09-01", 
"2016-10-01", "2016-11-01", "2016-12-01", "2017-01-01", "2017-02-01", 
"2017-03-01", "2017-04-01", "2017-05-01", "2017-06-01", "2017-07-01", 
"2017-08-01", "2017-09-01", "2017-10-01", "2017-11-01", "2017-12-01", 
"2018-01-01", "2018-02-01", "2018-03-01", "2018-04-01", "2018-05-01", 
"2018-06-01", "2018-07-01", "2018-08-01", "2018-09-01", "2018-10-01", 
"2018-11-01", "2018-12-01", "2019-01-01", "2019-02-01", "2019-03-01", 
"2019-04-01"), class = "factor"), IMPCH = c(293.1, 281, 293, 
283.3, 295.1, 348.7, 344.4, 311.8, 391.8, 385.5, 327.5, 306.5, 
459.5, 376.6, 401.8, 264.9, 319, 375.7, 450.2, 434.7, 413.4, 
398.5, 486, 390.7, 520.6, 565.3, 482.5, 468.3, 514.7, 536.3, 
560, 598.1, 549.6, 567.9, 489.8, 440.5, 652.8, 650.6, 509.9, 
551.9, 615.1, 720.8, 761.6, 803.9, 793.3, 834, 798.8, 818.2, 
788.9, 798.1, 667.3, 728.5, 937.9, 1021.7, 1162.7, 1279.6, 1179.3, 
1340.4, 1133.8, 951.5, 1186.1, 993.8, 931, 996.4, 1173.5, 1317.2, 
1492.5, 1568.6, 1432.1, 1652.1, 1367.9, 1126.2, 1321.6, 1253.7, 
974.3, 1104.2, 1380.8, 1525.5, 1813.2, 1872.4, 1936.3, 2236.4, 
1957.6, 1593.2, 1912.6, 1693.7, 1441.8, 1677.6, 1853.9, 2179.2, 
2503.8, 2613, 2760.5, 2748.4, 2316, 2027, 2187.6, 1862.4, 2083.2, 
2226.3, 2376.3, 2754.2, 2981.1, 3223.3, 3338.7, 3277.6, 2899.6, 
2329.6, 2763.1, 2499.2, 2183, 2491.6, 2979, 3463.3, 3645.4, 4165.8, 
4134.4, 4101.2, 3534.3, 2826.5, 3450.6, 3001.5, 2910.4, 3148.3, 
3654.9, 3960.7, 4311.8, 4804.7, 4584.1, 4714.3, 3868, 3133.9, 
3657.7, 3539.6, 2863.7, 3247.9, 3954.3, 4111.2, 4816.7, 5495.7, 
5480.7, 5812.9, 4585.4, 3947, 4667.6, 4262.4, 3628.6, 4445, 4795.1, 
5213.5, 5777.2, 6073.6, 6561.4, 6606.5, 5425.7, 5101.1, 5453.2, 
4559.6, 4798.1, 5262.9, 5539.4, 6020.2, 6556.2, 6779.9, 7125.2, 
7377.7, 6374.1, 5322.1, 5654, 5563.1, 5204, 5818.9, 6363.1, 7117.4, 
7405.7, 8022.1, 8198.2, 8207.9, 7543.5, 6690.3, 6902.1, 6584.4, 
6424.1, 7070.5, 7850.2, 8541.7, 9246.4, 10054, 10061.7, 10611.6, 
9066.8, 7604.7, 8427.5, 6375.6, 7590.2, 7686.8, 7757.9, 8398.2, 
8975.3, 10042.9, 9927.8, 10808.3, 8878.8, 7409.1, 8415.4, 8020.8, 
7259, 9097.6, 9846.9, 10727.2, 11213.2, 12671.4, 12291.5, 11455, 
12569.6, 11625, 11403.497575, 9629.62711, 10110.044562, 11521.852382, 
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