Ventas de tractocamiones en México: modelo de regresión a base de indicadores macroeconómicos
Singla, Martin (Frost & Sullivan, Mobility, LATAM)
29/4/2020
data_tractos <-read.csv("/Users/martinsingla/Desktop/Mexico_tractos_data.csv")#DATOS
data_tractos$year_quarter <- as.yearqtr(data_tractos$year_quarter)#MODELO DE REGRESIÓN (A: Serie 2008-2019)
tractos_reg1 <- lm(tracto_sales_quarterly ~ gdp_manufacturing + gdp_current_prices + gdp_foodnbev + construction_prod_value + wholesale_sales_index + retail_sales_index + exports + imports + private_consumption + gov_consumption + investment + inflation_rate + interest_rate + exchange_rate + stock_change_index + q2 + q3 + q4 + emission_norm18, data = data_tractos)
summary(tractos_reg1)##
## Call:
## lm(formula = tracto_sales_quarterly ~ gdp_manufacturing + gdp_current_prices +
## gdp_foodnbev + construction_prod_value + wholesale_sales_index +
## retail_sales_index + exports + imports + private_consumption +
## gov_consumption + investment + inflation_rate + interest_rate +
## exchange_rate + stock_change_index + q2 + q3 + q4 + emission_norm18,
## data = data_tractos)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1016.22 -229.80 22.55 261.33 664.32
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -25440.7876633 6253.9685980 -4.068 0.000350 ***
## gdp_manufacturing -0.0018829 0.0015522 -1.213 0.235257
## gdp_current_prices -0.0006963 0.0005829 -1.195 0.242290
## gdp_foodnbev 0.0007140 0.0091479 0.078 0.938343
## construction_prod_value 0.0709499 0.0341852 2.075 0.047245 *
## wholesale_sales_index -54.8279836 71.1682588 -0.770 0.447515
## retail_sales_index 297.9535121 79.9801882 3.725 0.000873 ***
## exports 0.0264182 0.0587248 0.450 0.656272
## imports 0.0556521 0.0638588 0.871 0.390900
## private_consumption 0.0010825 0.0008981 1.205 0.238200
## gov_consumption -0.0042136 0.0049976 -0.843 0.406302
## investment -0.0006863 0.0014246 -0.482 0.633707
## inflation_rate 13883.0468667 20314.0113094 0.683 0.499957
## interest_rate -80.9868598 208.8367754 -0.388 0.701097
## exchange_rate 113.3186516 216.1278931 0.524 0.604187
## stock_change_index 0.0733078 0.0427849 1.713 0.097691 .
## q2 309.1066638 339.1210398 0.911 0.369816
## q3 -295.6913081 359.9437669 -0.821 0.418306
## q4 -34.0060563 672.5621112 -0.051 0.960034
## emission_norm18 1445.3266585 553.4044754 2.612 0.014319 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 483.4 on 28 degrees of freedom
## (24 observations deleted due to missingness)
## Multiple R-squared: 0.9012, Adjusted R-squared: 0.8342
## F-statistic: 13.45 on 19 and 28 DF, p-value: 0.00000000191reg1_results <- as.data.frame(residuals(tractos_reg1))
reg1_results$residuos <- reg1_results$`residuals(tractos_reg1)`
reg1_results$`residuals(tractos_reg1)` <- NULL
reg1_results$predicts <- predict(tractos_reg1)
reg1_results$valores_observados <- data_tractos[25:72, 24]
reg1_results$year_quarter <- data_tractos[25:72, 3]#VISUALIZACIÓN DE MODELO de REG. MÚLTIPLE (A)
ggplot() +
geom_line(data = reg1_results, aes(x= year_quarter,y= valores_observados, color = "Ventas históricas")) +
geom_line(data = reg1_results, aes(x= year_quarter, y= predicts, color = "Ventas modeladas")) +
labs(title= "(A) Ventas de tractocamiones en México (2008-2019)",
subtitle= "Ventas históricas observadas vs. modeladas (serie trimestral)",
y = "ventas tractocamiones",
x = "Año / Trimestre",
color = "Series") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
#TEST DE AUTOCORRELACIÓN DE RESIDUOS (A)
checkresiduals(tractos_reg1)
##
## Breusch-Godfrey test for serial correlation of order up to 23
##
## data: Residuals
## LM test = 41.641, df = 23, p-value = 0.009993Los residuos se distribuyen normalmente y el test ACF muestra que no hay auto-correlación de residuos. Esto nos indica que el comportamiento de los residuos es aleatorio y no responde al de alguna variable que no se esté contemplando.
#MODELO DE REGRESIÓN (B: Serie 2002-2019)
tractos_reg2 <- lm(tracto_sales_quarterly ~ gdp_manufacturing + gdp_current_prices + gdp_foodnbev + exports + imports + private_consumption + gov_consumption + investment + inflation_rate + interest_rate + exchange_rate + stock_change_index + q2 + q3 + q4 + emission_norm18, data = data_tractos)
summary(tractos_reg2)##
## Call:
## lm(formula = tracto_sales_quarterly ~ gdp_manufacturing + gdp_current_prices +
## gdp_foodnbev + exports + imports + private_consumption +
## gov_consumption + investment + inflation_rate + interest_rate +
## exchange_rate + stock_change_index + q2 + q3 + q4 + emission_norm18,
## data = data_tractos)
##
## Residuals:
## Min 1Q Median 3Q Max
## -1115.23 -318.36 47.04 346.57 1139.06
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -3423.4103213 1543.6306859 -2.218 0.03072 *
## gdp_manufacturing 0.0021729 0.0010962 1.982 0.05245 .
## gdp_current_prices -0.0011564 0.0005297 -2.183 0.03332 *
## gdp_foodnbev -0.0170306 0.0064738 -2.631 0.01103 *
## exports 0.1218323 0.0513239 2.374 0.02113 *
## imports -0.0629820 0.0563860 -1.117 0.26886
## private_consumption 0.0020060 0.0006500 3.086 0.00317 **
## gov_consumption -0.0023959 0.0030965 -0.774 0.44239
## investment 0.0006543 0.0009752 0.671 0.50504
## inflation_rate 21390.6646044 16681.7259997 1.282 0.20512
## interest_rate 111.1524355 109.3106697 1.017 0.31368
## exchange_rate 243.8185438 189.8433552 1.284 0.20442
## stock_change_index 0.0872203 0.0299745 2.910 0.00521 **
## q2 730.8545629 299.4110771 2.441 0.01789 *
## q3 480.6158720 278.5527104 1.725 0.09007 .
## q4 821.3682950 375.2273307 2.189 0.03286 *
## emission_norm18 1355.3493204 526.0293239 2.577 0.01269 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 571 on 55 degrees of freedom
## Multiple R-squared: 0.8419, Adjusted R-squared: 0.7959
## F-statistic: 18.3 on 16 and 55 DF, p-value: < 0.00000000000000022Se quitó de la serie los indicadores “construction_prod_value”, “wholesale_sales_index” y “retail_sales_index”, debido a la falta de datos para toda la serie histórica de “tracto_sales_quarterly”. Esto nos permite abarcar el período 2001-2019.
##VISUALIZACIÓN DE MODELO de REG. MÚLTIPLE (B)
reg2_results <- as.data.frame(residuals(tractos_reg2))
reg2_results$residuos <- reg2_results$`residuals(tractos_reg2)`
reg2_results$`residuals(tractos_reg2)` <- NULL
reg2_results$predicts <- predict(tractos_reg2)
reg2_results$valores_observados <- data_tractos[0:72, 24]
reg2_results$year_quarter <- data_tractos[0:72, 3]ggplot() +
geom_line(data = reg2_results, aes(x= year_quarter,y= valores_observados, color = "Ventas históricas")) +
geom_line(data = reg2_results, aes(x= year_quarter, y= predicts, color = "Ventas modeladas")) +
labs(title= "(B) Ventas de tractocamiones en México (2002-2019)",
subtitle= "Ventas históricas observadas vs. modeladas (serie trimestral)",
y = "ventas tractocamiones",
x = "Año / Trimestre",
color = "Series") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
#TEST DE AUTOCORRELACIÓN DE RESIDUOS (B)
checkresiduals(tractos_reg2)
##
## Breusch-Godfrey test for serial correlation of order up to 20
##
## data: Residuals
## LM test = 30.375, df = 20, p-value = 0.064Los residuos se distribuyen de forma normal, sin embargo el test ACF indica valores extremos en el Lag 1, lo cual puede estar indicando cierto nivel de auto-correlación, que disminuía cuando incluíamos las variables eliminadas, por lo que puede ser desestimado.
#MODELO DE REGRESIÓN AJUSTADO (C: Serie 2008-2019)
tractos_reg3 <- lm(tracto_sales_quarterly ~ gdp_manufacturing + gdp_current_prices + construction_prod_value + retail_sales_index + exports + imports + private_consumption + gov_consumption + stock_change_index + q2 + q3 + q4 + emission_norm18, data = data_tractos)
summary(tractos_reg3)##
## Call:
## lm(formula = tracto_sales_quarterly ~ gdp_manufacturing + gdp_current_prices +
## construction_prod_value + retail_sales_index + exports +
## imports + private_consumption + gov_consumption + stock_change_index +
## q2 + q3 + q4 + emission_norm18, data = data_tractos)
##
## Residuals:
## Min 1Q Median 3Q Max
## -990.3 -252.3 -31.7 287.6 897.6
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -23752.8679962 3957.0316540 -6.003 0.000000854 ***
## gdp_manufacturing -0.0016397 0.0012653 -1.296 0.20373
## gdp_current_prices -0.0008258 0.0004783 -1.727 0.09333 .
## construction_prod_value 0.0509530 0.0204019 2.497 0.01751 *
## retail_sales_index 243.8758001 47.0655256 5.182 0.000009984 ***
## exports 0.0257459 0.0378076 0.681 0.50050
## imports 0.0269743 0.0402577 0.670 0.50736
## private_consumption 0.0012233 0.0006191 1.976 0.05633 .
## gov_consumption -0.0031089 0.0013248 -2.347 0.02490 *
## stock_change_index 0.0722213 0.0232456 3.107 0.00380 **
## q2 397.0323008 236.4208940 1.679 0.10225
## q3 18.9736443 231.2908390 0.082 0.93510
## q4 640.3295705 338.0081906 1.894 0.06670 .
## emission_norm18 1479.2112119 421.7208142 3.508 0.00129 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 457.4 on 34 degrees of freedom
## (24 observations deleted due to missingness)
## Multiple R-squared: 0.8926, Adjusted R-squared: 0.8516
## F-statistic: 21.74 on 13 and 34 DF, p-value: 0.0000000000009764#Quito “GDP_foodnbev”, “investment”, “exchange_rate”, “interest_rate” , “wholesales_index” e “inflation”
reg3_results <- as.data.frame(residuals(tractos_reg3))
reg3_results$residuos <- reg3_results$`residuals(tractos_reg3)`
reg3_results$`residuals(tractos_reg3)` <- NULL
reg3_results$predicts <- predict(tractos_reg3)
reg3_results$valores_observados <- data_tractos[25:72, 24]
reg3_results$year_quarter <- data_tractos[25:72, 3]#VISUALIZACIÓN DE MODELO de REG. MÚLTIPLE (C)
ggplot() +
geom_line(data = reg3_results, aes(x= year_quarter,y= valores_observados, color = "Ventas históricas")) +
geom_line(data = reg3_results, aes(x= year_quarter, y= predicts, color = "Ventas modeladas")) +
labs(title= "(C) Ventas de tractocamiones en México (2008-2019)",
subtitle= "Ventas históricas observadas vs. modeladas (serie trimestral)",
y = "ventas tractocamiones",
x = "Año / Trimestre",
color = "Series") +
theme(axis.text.x = element_text(angle = 45, hjust = 1))
#TEST DE AUTOCORRELACIÓN DE RESIDUOS (C)
checkresiduals(tractos_reg3)
##
## Breusch-Godfrey test for serial correlation of order up to 17
##
## data: Residuals
## LM test = 27.261, df = 17, p-value = 0.05436