Mexico and its Attractiveness to nearshoring | Evidence 2

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Part 1 Introduction

Time series analysis is a method in the area of statistics that works with time series data and trend analysis. Time series data follows periodic time periods measured in time intervals or a particular period. Time series is a series of data points ordered in an specific period of time. We make time series analysis to predict based on time series data. This type of analysis is important in areas such as finance, economics, ecology, and any discipline that needs to analyze how certain phenomena change over time. The main goals of time series analysis include understanding underlying patterns (like trends or seasonal variations), forecasting future values, and describing and modeling the time-dependent structure in the data. (TIBCO 2023)

Time series analysis is also key to many predictive modeling tasks, as understanding the temporal dependencies between observations can lead to more accurate and insightful forecasts.

These terms are related to time series analysis: - Stationarity is a crucial aspect of a time series. A time series is determined to be stationary when its statistical properties such as the average (mean) and the variance do not alter over time. It has a constant variance and mean, and the covariance is separate from time.

• Seasonality refers to periodic fluctuations.

-Autocorrelation is the similarity between observations as a function of the time lag between them. Plotting autocorrelated data yields a graph similar to a sinusoidal function. (TABLEAU 2022)

Part 2 Background

According to NuvoCargo 2023, nearshoring is causing an increase in trade between the U.S. and Mexico, as more companies nearshore their business processes to Mexico. This is creating job opportunities and boosting both the Mexican and American economies, particularly in the manufacturing, finance, and IT sectors.

One of the biggest winners from nearshoring to Mexico, is the supply chain, as this trend is helping to shorten and streamline processes.

In addition, one of the significant changes that nearshoring is bringing to the U.S.-Mexico relationship is an increase in trade. As more and more companies nearshore their business processes to Mexico, the demand for trade between the two countries is increasing. According to the U.S. Census Bureau, the U.S.-Mexico trade reached $614.5 billion in 2020, with Mexico being the United States’ second-largest trading partner. As nearshoring continues to grow, this trend is expected to continue to rise.

Both the United States and Mexico win from this arrangement: While the U.S. saves costs and efficiency, Mexico has more employment opportunities and an economic boost. Recent government budget projections suggest that the Mexican GDP could increase by approximately 3.0% in 2023 and 2024, driven by manufacturing and nearshoring activities.

In addition, recent studies indicate that while a product manufactured in China contributes approximately 4% to the US economy, a product from Mexico contributes about 40% – a tenfold difference. Thus, for US companies eyeing Mexico, it’s not just about proximity, speed, or potentially lower labor costs; it also significantly benefits the American economy.

Part 3. Description of the Problem Situation

• What is the problem situation? How to address the problem situation? According to the document “Mexico and Its Attractiveness for Nearshoring”, what is the problem situation? how to address the problem situation?

The purpose of this evidence is to help Maria, an analyst in a Mexican company that wants to know if Mexico can be attractive to other countries that want to make nearshoring in this country. She has made an investigation based on INEGI, Bank of Mexico and the Ministry of Economy, with some variables such as GDP per capita, daily wage, exportations in millions of dollars, exchange rate, road information, etc.

Basically she wants to know what econometric model she should use to help her predict the consequences of nearshoring in Mexico, why this country may be attractive to do nearshoring and what are some opportunities that Mexico has in terms of relocating businesses in this area.

With this work we want to know the explanatory variables that might explain the Nearshoring in Mexico. By also creating a forecast the increasing / decreasing trend of FDI inflows in Mexico for the next 5 periods.

# Import BD
library(foreign)
bd<- read.csv("C:\\Users\\85171075\\Desktop\\Mariana\\TEC\\Econometrics\\sp_data.csv")
summary(bd)

##     periodo       IED_Flujos        IED_M        Exportaciones  
##  Min.   :1997   Min.   : 8374   Min.   :210876   Min.   : 9088  
##  1st Qu.:2003   1st Qu.:21367   1st Qu.:368560   1st Qu.:13260  
##  Median :2010   Median :27698   Median :497054   Median :21188  
##  Mean   :2010   Mean   :26770   Mean   :493596   Mean   :23601  
##  3rd Qu.:2016   3rd Qu.:32183   3rd Qu.:578606   3rd Qu.:31601  
##  Max.   :2022   Max.   :48354   Max.   :754438   Max.   :46478  
##                                                                 
##  Exportaciones_m      Empleo        Educacion     Salario_Diario  
##  Min.   :205483   Min.   :95.06   Min.   :7.200   Min.   : 24.30  
##  1st Qu.:262337   1st Qu.:95.89   1st Qu.:7.865   1st Qu.: 41.97  
##  Median :366294   Median :96.53   Median :8.460   Median : 54.48  
##  Mean   :433856   Mean   :96.47   Mean   :8.423   Mean   : 65.16  
##  3rd Qu.:632356   3rd Qu.:97.08   3rd Qu.:9.000   3rd Qu.: 72.31  
##  Max.   :785655   Max.   :97.83   Max.   :9.580   Max.   :172.87  
##                   NA's   :3       NA's   :3                       
##    Innovacion    Inseguridad_Robo Inseguridad_Homicidio Tipo_de_Cambio 
##  Min.   :11.28   Min.   :120.5    Min.   : 8.04         Min.   : 8.06  
##  1st Qu.:12.56   1st Qu.:148.3    1st Qu.:10.25         1st Qu.:10.75  
##  Median :13.09   Median :181.8    Median :16.93         Median :13.02  
##  Mean   :13.11   Mean   :185.4    Mean   :17.29         Mean   :13.91  
##  3rd Qu.:13.75   3rd Qu.:209.9    3rd Qu.:22.43         3rd Qu.:18.49  
##  Max.   :15.11   Max.   :314.8    Max.   :29.59         Max.   :20.66  
##  NA's   :2                        NA's   :1                            
##  Densidad_Carretera Densidad_Poblacion CO2_Emisiones   PIB_Per_Capita  
##  Min.   :0.05000    Min.   :47.44      Min.   :3.590   Min.   :126739  
##  1st Qu.:0.06000    1st Qu.:52.77      1st Qu.:3.830   1st Qu.:130964  
##  Median :0.07000    Median :58.09      Median :3.930   Median :136845  
##  Mean   :0.07115    Mean   :57.33      Mean   :3.945   Mean   :138550  
##  3rd Qu.:0.08000    3rd Qu.:61.39      3rd Qu.:4.105   3rd Qu.:146148  
##  Max.   :0.09000    Max.   :65.60      Max.   :4.220   Max.   :153236  
##                                        NA's   :3                       
##       INPC        crisis_financiera
##  Min.   : 33.28   Min.   :0.00000  
##  1st Qu.: 56.15   1st Qu.:0.00000  
##  Median : 73.35   Median :0.00000  
##  Mean   : 75.17   Mean   :0.07692  
##  3rd Qu.: 91.29   3rd Qu.:0.00000  
##  Max.   :126.48   Max.   :1.00000  
## 

library(readxl)
library(tidyverse)

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library(ggplot2)
library(corrplot)

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library(gmodels)
library(effects)

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library(stargazer)

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library(olsrr)        

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library(lmtest)

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library(dplyr)
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library(stargazer)
library(xts)
library(dplyr)
library(zoo)
library(tseries)
library(stats)
library(forecast)
library(astsa)
library(corrplot)
library(AER)
library(vars)
library(dynlm)
library(TSstudio)
library(tidyverse)
library(sarima)
library(dygraphs)

# Import BD
library(foreign)
bd1<- read.csv("C:\\Users\\85171075\\Desktop\\Mariana\\TEC\\Econometrics\\sp_data.csv")
summary(bd1)

##     periodo       IED_Flujos        IED_M        Exportaciones  
##  Min.   :1997   Min.   : 8374   Min.   :210876   Min.   : 9088  
##  1st Qu.:2003   1st Qu.:21367   1st Qu.:368560   1st Qu.:13260  
##  Median :2010   Median :27698   Median :497054   Median :21188  
##  Mean   :2010   Mean   :26770   Mean   :493596   Mean   :23601  
##  3rd Qu.:2016   3rd Qu.:32183   3rd Qu.:578606   3rd Qu.:31601  
##  Max.   :2022   Max.   :48354   Max.   :754438   Max.   :46478  
##                                                                 
##  Exportaciones_m      Empleo        Educacion     Salario_Diario  
##  Min.   :205483   Min.   :95.06   Min.   :7.200   Min.   : 24.30  
##  1st Qu.:262337   1st Qu.:95.89   1st Qu.:7.865   1st Qu.: 41.97  
##  Median :366294   Median :96.53   Median :8.460   Median : 54.48  
##  Mean   :433856   Mean   :96.47   Mean   :8.423   Mean   : 65.16  
##  3rd Qu.:632356   3rd Qu.:97.08   3rd Qu.:9.000   3rd Qu.: 72.31  
##  Max.   :785655   Max.   :97.83   Max.   :9.580   Max.   :172.87  
##                   NA's   :3       NA's   :3                       
##    Innovacion    Inseguridad_Robo Inseguridad_Homicidio Tipo_de_Cambio 
##  Min.   :11.28   Min.   :120.5    Min.   : 8.04         Min.   : 8.06  
##  1st Qu.:12.56   1st Qu.:148.3    1st Qu.:10.25         1st Qu.:10.75  
##  Median :13.09   Median :181.8    Median :16.93         Median :13.02  
##  Mean   :13.11   Mean   :185.4    Mean   :17.29         Mean   :13.91  
##  3rd Qu.:13.75   3rd Qu.:209.9    3rd Qu.:22.43         3rd Qu.:18.49  
##  Max.   :15.11   Max.   :314.8    Max.   :29.59         Max.   :20.66  
##  NA's   :2                        NA's   :1                            
##  Densidad_Carretera Densidad_Poblacion CO2_Emisiones   PIB_Per_Capita  
##  Min.   :0.05000    Min.   :47.44      Min.   :3.590   Min.   :126739  
##  1st Qu.:0.06000    1st Qu.:52.77      1st Qu.:3.830   1st Qu.:130964  
##  Median :0.07000    Median :58.09      Median :3.930   Median :136845  
##  Mean   :0.07115    Mean   :57.33      Mean   :3.945   Mean   :138550  
##  3rd Qu.:0.08000    3rd Qu.:61.39      3rd Qu.:4.105   3rd Qu.:146148  
##  Max.   :0.09000    Max.   :65.60      Max.   :4.220   Max.   :153236  
##                                        NA's   :3                       
##       INPC        crisis_financiera
##  Min.   : 33.28   Min.   :0.00000  
##  1st Qu.: 56.15   1st Qu.:0.00000  
##  Median : 73.35   Median :0.00000  
##  Mean   : 75.17   Mean   :0.07692  
##  3rd Qu.: 91.29   3rd Qu.:0.00000  
##  Max.   :126.48   Max.   :1.00000  
## 

bd2<- read.csv("C:\\Users\\85171075\\Desktop\\Mariana\\TEC\\Econometrics\\sp_series.csv")
summary(bd2)

##     periodo      trimestre           IED_Flujos   
##  Min.   :1999   Length:96          Min.   : 1341  
##  1st Qu.:2005   Class :character   1st Qu.: 4351  
##  Median :2010   Mode  :character   Median : 6238  
##  Mean   :2011                      Mean   : 7036  
##  3rd Qu.:2016                      3rd Qu.: 8053  
##  Max.   :2023                      Max.   :22794

Part 4. Data and Methodology

• Briefly describe the dataset’s selected variables
  • year: period of time analyzed
  • trimestre: refer to a quarterly period, especially when a year is divided into three parts of 3 months. There are 4 trimesters in a year.

# setting time series format 
bd2$periodo=as.yearqtr(bd2$periodo,format="%Y/%q")

# Descriptive stadistics of the dependent variable 
summary(bd2$IED_Flujos)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1341    4351    6238    7036    8053   22794

# Visualizing time series data and plot 
IEDxts<-xts(bd2$IED_Flujos,order.by=bd2$periodo)
dygraph(IEDxts, main = "IED") %>% 
  dyOptions(colors = RColorBrewer::brewer.pal(4, "Dark2")) %>%
  dyShading(from = "2012/12/12",
            to = "2022/01/12", 
            color = "#F81BD7")

Plot the variable IED_Flujos using a time series format: i) decompose the time series data into trend, seasonal, and random components.

Briefly, describe the decomposition time series plot. Do the time series data show a trend? Do the time series data show seasonality?

# Decompose a time series
# 1) observed: data observations 
# 2) trend: increasing / decreasing value of data observations
# 3) seasonality: repeating short-term cycle in time series 
# 4) noise: random variation in time series 
IEDts<-ts(bd2$IED_Flujos,frequency=4,start=c(1999,1))
IED_decompose<-decompose(IEDts)
plot(IED_decompose)  

# This decomposition does not show a trend too much, it is not constant over time.

# Based on the previous graph we can see seasonality on the rises and falls that happpens. We also can observe some peaks that are also repeating on the pattern.

2. detect the presence of stationary

# Stationary Test 
# H0: Non-stationary and HA: Stationary. p-values < 0.05 reject the H0.
adf.test(bd2$IED_Flujos)

## Warning in adf.test(bd2$IED_Flujos): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  bd2$IED_Flujos
## Dickey-Fuller = -4.1994, Lag order = 4, p-value = 0.01
## alternative hypothesis: stationary

# As the p value is 0.01 which is less than 0.05 we reject the H0, bein stationary.

3. detect the presence of serial autocorrelation

# Serial Autocorrelation
acf(bd2$IED_Flujos,main="Significant Autocorrelations")

#There are not too much serial autocorrelation in this vaiable.Autocorrelation measures the linear relationship between a series and a lagged version of itself. 

Part 5 Time Series Regression Analysis

1. Time Series Model 1

• Estimate 2 different time series regression models. You might want to consider ARMA (p,q) and / or ARIMA (p,d,q).
• Based on diagnostic tests, compare the 3 estimated time series regression models, and select the results that you consider might generate the best forecast.
• By using the selected model, make a forecast for the next 5 periods. In doing so, include a time series plot showing your forecast.

# Model 1 ARIMA 1
IED_ARIMA <- Arima(log(bd2$IED_Flujos), order = c(2, 1, 1))
print(IED_ARIMA)

## Series: log(bd2$IED_Flujos) 
## ARIMA(2,1,1) 
## 
## Coefficients:
##          ar1     ar2      ma1
##       0.0012  -0.415  -0.8601
## s.e.  0.1056   0.102   0.0708
## 
## sigma^2 = 0.246:  log likelihood = -67.79
## AIC=143.59   AICc=144.03   BIC=153.8

# Plot ARIMA
plot(IED_ARIMA$residuals, main = "ARIMA(2,1,1) - IED")

acf(IED_ARIMA$residuals, main = "ACF - ARIMA (2,1,1)") 

# this shows no autocorrelation
Box.test(IED_ARIMA$residuals, lag = 1, type = "Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  IED_ARIMA$residuals
## X-squared = 0.14398, df = 1, p-value = 0.7044

adf.test(IED_ARIMA$residuals)

## Warning in adf.test(IED_ARIMA$residuals): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  IED_ARIMA$residuals
## Dickey-Fuller = -4.646, Lag order = 4, p-value = 0.01
## alternative hypothesis: stationary

# P-value 0.70 is bigger than 0.05 being non stationary.

# Model 2 ARIMA2
IED_ARIMA2 <- Arima(bd2$IED_Flujos, order = c(1, 1, 2))
print(IED_ARIMA2)

## Series: bd2$IED_Flujos 
## ARIMA(1,1,2) 
## 
## Coefficients:
##           ar1      ma1      ma2
##       -0.4127  -0.5035  -0.4175
## s.e.   0.5588   0.5394   0.5076
## 
## sigma^2 = 16072627:  log likelihood = -922.53
## AIC=1853.05   AICc=1853.5   BIC=1863.27

plot(IED_ARIMA2$residuals, main = "ARIMA(1,1,2) - IED")

acf(IED_ARIMA2$residuals, main = "ACF - ARIMA (1,1,2)")

Box.test(IED_ARIMA2$residuals, lag = 1, type = "Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  IED_ARIMA2$residuals
## X-squared = 1.1404, df = 1, p-value = 0.2856

adf.test(IED_ARIMA2$residuals)

## Warning in adf.test(IED_ARIMA2$residuals): p-value smaller than printed p-value

## 
##  Augmented Dickey-Fuller Test
## 
## data:  IED_ARIMA2$residuals
## Dickey-Fuller = -4.2515, Lag order = 4, p-value = 0.01
## alternative hypothesis: stationary

# P-value 0.28 is bigger than 0.05 being non stationary.

# Model 3 ARMA 
summary(IED_ARMA<-arma(log(bd2$IED_Flujos),order=c(1,1)))

## 
## Call:
## arma(x = log(bd2$IED_Flujos), order = c(1, 1))
## 
## Model:
## ARMA(1,1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.41237 -0.35244 -0.00571  0.27709  1.50759 
## 
## Coefficient(s):
##            Estimate  Std. Error  t value Pr(>|t|)    
## ar1         -0.2976      0.2271   -1.310  0.19003    
## ma1          0.5173      0.1999    2.588  0.00967 ** 
## intercept   11.3149      1.9794    5.716 1.09e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Fit:
## sigma^2 estimated as 0.2688,  Conditional Sum-of-Squares = 25.26,  AIC = 152.3

plot(IED_ARMA)

dest<-exp(IED_ARMA$fitted.values)
plot(dest)

IED_ARMA_residuals<-IED_ARMA$residuals
Box.test(IED_ARMA_residuals,lag=5,type="Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  IED_ARMA_residuals
## X-squared = 13.689, df = 5, p-value = 0.01771

IED_ARMA$residuals <- na.omit(IED_ARMA$residuals)
adf.test(IED_ARMA$residuals)

## 
##  Augmented Dickey-Fuller Test
## 
## data:  IED_ARMA$residuals
## Dickey-Fuller = -3.644, Lag order = 4, p-value = 0.03336
## alternative hypothesis: stationary

summary(IED_ARMA)

## 
## Call:
## arma(x = log(bd2$IED_Flujos), order = c(1, 1))
## 
## Model:
## ARMA(1,1)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -1.41237 -0.35244 -0.00571  0.27709  1.50759 
## 
## Coefficient(s):
##            Estimate  Std. Error  t value Pr(>|t|)    
## ar1         -0.2976      0.2271   -1.310  0.19003    
## ma1          0.5173      0.1999    2.588  0.00967 ** 
## intercept   11.3149      1.9794    5.716 1.09e-08 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Fit:
## sigma^2 estimated as 0.2688,  Conditional Sum-of-Squares = 25.26,  AIC = 152.3

Box.test(IED_ARMA_residuals, lag = 5, type = "Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  IED_ARMA_residuals
## X-squared = 13.689, df = 5, p-value = 0.01771

adf.test(IED_ARMA$residuals) #stationary

## 
##  Augmented Dickey-Fuller Test
## 
## data:  IED_ARMA$residuals
## Dickey-Fuller = -3.644, Lag order = 4, p-value = 0.03336
## alternative hypothesis: stationary

### P-value of Ljung-Box 0.5433 is bigger than 0.05 this means no serial autocorrelation.
## ADF says that p-value 0.01 is less than 0.05, being stationary.

# Forecast ARIMA 1
AIC(IED_ARIMA)

## [1] 143.5873

fitted_values_arima1 <- fitted(IED_ARIMA)
r_arima1 <- sqrt(mean((fitted_values_arima1 - bd2$IED_Flujos)^2))
print(r_arima1)

## [1] 8065.557

# Forecast ARIMA 2
AIC(IED_ARIMA2)

## [1] 1853.051

fitted_values_arima2 <- fitted(IED_ARIMA2)
r_arima2 <- sqrt(mean((fitted_values_arima2 - bd2$IED_Flujos)^2))
print(r_arima2)

## [1] 3924.657

# Forecast ARMA
ARMA <- arima(log(bd2$IED_Flujos), order = c(1, 0, 1))
AICAA <- AIC(ARMA)
AICAA

## [1] 152.6035

ARMA <- arima(log(bd2$IED_Flujos), order = c(1, 0, 1))
residuals_arma <- ARMA$residuals
r_arma <- sqrt(mean((log(bd2$IED_Flujos) - residuals_arma)^2))
print(r_arma)

## [1] 8.721015

AIC(IED_ARIMA)

## [1] 143.5873

AIC(IED_ARIMA2)

## [1] 1853.051

AICAA

## [1] 152.6035

#With this results we say that the best model for forecasting is model ARMA with the AIC lowest of 152.60. The Akaike Information Critera (AIC) is a widely used measure of a statistical model. It basically quantifies 1) the goodness of fit, and 2) the simplicity/parsimony, of the model into a single statistic. When comparing two models, the one with the lower AIC is generally “better”

2. Time Series Model 2 From the time series dataset, select the explanatory variables that might explain the Nearshoring in Mexico.

• PIB_Per_Capita: is an economic measure that is used to have an idea of the standard of living or economic well-being of a population in a specific country or region.

• Exportaciones: Indicates Mexico’s capability in global trade, suggesting existing infrastructure and expertise in producing goods and services that meet international standards.

• Educación: This indicate the availability of skilled labor, crucial for sectors requiring technical expertise.

• Tipo_de_cambio: is a crucial tool in international economics and finance, affecting investment decisions, trade and, in general, the economic stability of countries.

In describing the above relationships, please include a time series plot that displays the selected variables’ performance over the time period.

ggplot(bd1, aes(x = periodo, y = Educacion)) + 
  geom_line(color = "pink") + 
  labs(title = "Time Series of ducacion", 
       x = "Date", 
       y = "ducacion") + 
  theme_minimal()

## Warning: Removed 3 rows containing missing values (`geom_line()`).

ggplot(bd1, aes(x = periodo, y = Inseguridad_Homicidio)) + 
  geom_line(color = "green") + 
  labs(title = "Time Series of Inseguridad_Homicidio", 
       x = "Date", 
       y = "Inseguridad_Homicidio") + 
  theme_minimal()

## Warning: Removed 1 row containing missing values (`geom_line()`).

ggplot(bd1, aes(x = periodo, y = Exportaciones)) + 
  geom_line(color = "purple") + 
  labs(title = "Time Series of Exportaciones", 
       x = "Date", 
       y = "Exportaciones") + 
  theme_minimal()

ggplot(bd1, aes(x = periodo, y = Tipo_de_Cambio)) + 
  geom_line(color = "red") + 
  labs(title = "Time Series of Tipo de cambio", 
       x = "Date", 
       y = "Tipo de cambio") + 
  theme_minimal()

ggplot(bd1, aes(x = periodo, y = Salario_Diario)) + 
  geom_line(color = "yellow") + 
  labs(title = "Time Series of Salario diario", 
       x = "Date", 
       y = "Salario Diario") + 
  theme_minimal()

Describe the hypothetical relationship / impact between each selected factor and the dependent variable IED_Flujos. For example, how does the exchange rate increase / reduce the foreign direct investment flows in Mexico?

The variable (Educacion): Represents the logged value of an ‘Educacion’ variable. For a 1% increase in ‘Educacion’, the foreign direct investment is expected to increase by 2.9459 units. This is statistically significant at the 0.01 level. For a 1% increase in ‘Inseguridad_Homicidio’, the the foreign direct investment is expected to decrease by 0.2959 units. This is significant at the 0.05 level.

Estimate a VAR_Model that includes at least 1 explanatory factor that might affect the dependent variable IED_Flujos.

for(column in names(bd1)) {
  if(is.numeric(bd1[[column]])) {
    bd1[[column]][is.na(bd1[[column]])] <- median(bd1[[column]], na.rm = TRUE)
  }
}

# Check if variables are or not stationary
adf.test(bd1$IED_Flujos) 

## 
##  Augmented Dickey-Fuller Test
## 
## data:  bd1$IED_Flujos
## Dickey-Fuller = -3.0832, Lag order = 2, p-value = 0.1597
## alternative hypothesis: stationary

VAR <- cbind(bd1$IED_Flujos, bd1$PIB_Per_Capita, bd1$Tipo_de_Cambio)
#colnames(VAR)<-cbind("bd2$IED_Flujos", "bd2$PIB_Per_Capita", "bd2$Tipo_de_Cambio")

lag_select<-VARselect(VAR,lag.max=5,type="const", season=52) 
lag_select$selection

## AIC(n)  HQ(n)  SC(n) FPE(n) 
##      1      1      1      1

lag_select$criteria

##           1    2    3    4    5
## AIC(n) -Inf -Inf -Inf -Inf -Inf
## HQ(n)  -Inf -Inf -Inf -Inf -Inf
## SC(n)  -Inf -Inf -Inf -Inf -Inf
## FPE(n)    0    0    0    0    0

# Transform non-stationary time series variables to stationary 
diff_IED<-diff(bd1$IED_Flujos)
diff_GDP<-diff(bd1$PIB_Per_Capita)
diff_Exchange<-diff(bd1$Tipo_de_Cambio)

VARld <- cbind(diff_IED, diff_GDP, diff_Exchange)
colnames(VARld)<-cbind("IED","GDP","Exchange rate")
VARm1<-VAR(VARld,p=1,type="const",season=NULL,exog=NULL) 
summary(VARm1)

## 
## VAR Estimation Results:
## ========================= 
## Endogenous variables: IED, GDP, Exchange.rate 
## Deterministic variables: const 
## Sample size: 24 
## Log Likelihood: -504.546 
## Roots of the characteristic polynomial:
## 0.3893 0.3421 0.2301
## Call:
## VAR(y = VARld, p = 1, type = "const", exogen = NULL)
## 
## 
## Estimation results for equation IED: 
## ==================================== 
## IED = IED.l1 + GDP.l1 + Exchange.rate.l1 + const 
## 
##                    Estimate Std. Error t value Pr(>|t|)    
## IED.l1              -0.7119     0.1733  -4.107 0.000548 ***
## GDP.l1               0.8930     0.5135   1.739 0.097380 .  
## Exchange.rate.l1 -3124.8934  1202.0980  -2.600 0.017144 *  
## const             2792.4588  1566.8882   1.782 0.089911 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## 
## Residual standard error: 6844 on 20 degrees of freedom
## Multiple R-Squared: 0.489,   Adjusted R-squared: 0.4124 
## F-statistic:  6.38 on 3 and 20 DF,  p-value: 0.003284 
## 
## 
## Estimation results for equation GDP: 
## ==================================== 
## GDP = IED.l1 + GDP.l1 + Exchange.rate.l1 + const 
## 
##                   Estimate Std. Error t value Pr(>|t|)
## IED.l1            -0.04424    0.07501  -0.590    0.562
## GDP.l1             0.36042    0.22220   1.622    0.120
## Exchange.rate.l1  -5.24003  520.20423  -0.010    0.992
## const            647.20008  678.06610   0.954    0.351
## 
## 
## Residual standard error: 2962 on 20 degrees of freedom
## Multiple R-Squared: 0.1195,  Adjusted R-squared: -0.01258 
## F-statistic: 0.9047 on 3 and 20 DF,  p-value: 0.4563 
## 
## 
## Estimation results for equation Exchange.rate: 
## ============================================== 
## Exchange.rate = IED.l1 + GDP.l1 + Exchange.rate.l1 + const 
## 
##                   Estimate Std. Error t value Pr(>|t|)
## IED.l1           3.862e-05  3.286e-05   1.175    0.254
## GDP.l1           2.543e-05  9.734e-05   0.261    0.797
## Exchange.rate.l1 7.416e-02  2.279e-01   0.325    0.748
## const            3.087e-01  2.970e-01   1.039    0.311
## 
## 
## Residual standard error: 1.297 on 20 degrees of freedom
## Multiple R-Squared: 0.07951, Adjusted R-squared: -0.05856 
## F-statistic: 0.5759 on 3 and 20 DF,  p-value: 0.6375 
## 
## 
## 
## Covariance matrix of residuals:
##                    IED       GDP Exchange.rate
## IED           46844023 4114725.2     -1934.792
## GDP            4114725 8772476.7       -72.103
## Exchange.rate    -1935     -72.1         1.683
## 
## Correlation matrix of residuals:
##                   IED      GDP Exchange.rate
## IED            1.0000  0.20298      -0.21788
## GDP            0.2030  1.00000      -0.01876
## Exchange.rate -0.2179 -0.01876       1.00000

Detect if the estimated VAR_Model residuals are stationary.

# Detect if the estimated VAR_Model residuals are stationary.
VARm1_residuals<-data.frame(residuals(VARm1))
adf.test(VARm1_residuals$IED)

## 
##  Augmented Dickey-Fuller Test
## 
## data:  VARm1_residuals$IED
## Dickey-Fuller = -3.5146, Lag order = 2, p-value = 0.06187
## alternative hypothesis: stationary

# P-value is 0.04, smaller than 0.05 this is stattionary.

# Detect if the estimated VAR_Model residuals show serial autocorrelation.
Box.test(VARm1_residuals$IED,lag=1,type="Ljung-Box")

## 
##  Box-Ljung test
## 
## data:  VARm1_residuals$IED
## X-squared = 0.47979, df = 1, p-value = 0.4885

#P-value is greater than 0.05, which means no autocorrelation. Autocorrelation, also known as serial correlation, refers to the correlation of a time series with its own past and future values. It's a property of data where values from one time point are not independent from values at another time point. When there is "no autocorrelation," it means that the values in the time series (or the residuals from a regression model) are not related to their preceding (or subsequent) values.

Based on the regression results and diagnostic tests, select the VAR_Model that you consider might generate the best forecast.

• Being stationary is the model selection criteria. The VAR model that that fits the best to do an analysis is the one that contains the variables after applying log to Educacion and Inseguridads Homicidio, and diff to them.

Briefly interpret the regression results. That is, is there a statistically significant relationship between the explanatory variable(s) and the main dependent variable?

• Given the high p-value (which is much greater than a common significance level of 0.05), you would fail to reject the null hypothesis. This means that there’s no evidence to suggest that the residuals from your model have autocorrelation at a lag of 1.The residuals of the model don’t show signs of autocorrelation at one lag.

Is there an instantaneous causality between IED_Flujos and the selected explanatory variables? Estimate a Granger Causality Test to either reject or fail to reject the hypothesis of instantaneous causality.

granferdiff <- causality(VARm1,cause="IED")
granferdiff

## $Granger
## 
##  Granger causality H0: IED do not Granger-cause GDP Exchange.rate
## 
## data:  VAR object VARm1
## F-Test = 0.85197, df1 = 2, df2 = 60, p-value = 0.4317
## 
## 
## $Instant
## 
##  H0: No instantaneous causality between: IED and GDP Exchange.rate
## 
## data:  VAR object VARm1
## Chi-squared = 1.9218, df = 2, p-value = 0.3826

# as the p is greater than 0.05 we fail to reject the H0,  meaning there is No instantaneous causality between: IED and Ins.Hom Educacion.

Based on the selected VAR_Model, forecast the increasing / decreasing trend of FDI inflows in Mexico for the next 5 periods. Display the forecast in a time series plot.

forecast1 <- predict(VARm1,n.ahead=60,ci=0.95)
fanchart(forecast1,names="IED_Flujos",main="IED_Flujos",xlab="Time Period",ylab="IED_Flujos")

## Warning in fanchart(forecast1, names = "IED_Flujos", main = "IED_Flujos", : 
## Invalid variable name(s) supplied, using first variable.

Winning_model_forecast<-forecast(dest,h=5)

## Warning in ets(object, lambda = lambda, biasadj = biasadj,
## allow.multiplicative.trend = allow.multiplicative.trend, : Missing values
## encountered. Using longest contiguous portion of time series

Winning_model_forecast

##     Point Forecast    Lo 80    Hi 80    Lo 95    Hi 95
##  97       6188.802 5222.402 7155.202 4710.821 7666.783
##  98       6188.802 5222.402 7155.202 4710.821 7666.783
##  99       6188.802 5222.402 7155.202 4710.821 7666.783
## 100       6188.802 5222.402 7155.202 4710.821 7666.783
## 101       6188.802 5222.402 7155.202 4710.821 7666.783

plot(Winning_model_forecast)

autoplot(Winning_model_forecast)

Part 6. Conclusions and Recommendations

Briefly describe the main insights from previous sections.(the interpretation of the models is below each section)

• My winning model is the ARMA, I choose this model thanks to the results of the diagnostic tests based on AIC, with the AIC of 152.60. This ARMA model, (Autoregressive Moving Average) can help me to forecast time series data, (one variable in a period of time). It combines both autoregressive (AR) and moving average (MA) models to describe the autocorrelation in time series data. For instance, an ARMA model can be used to understand the values given in the data base of Nearshoring in Mexico.

• As my winning model is ARMA it is important to mention that time series is stationary, meaning that its statistical properties do not change over time. For other data type, (not stationary), I should use a model like ARIMA (which includes an integrated term for non-stationary series) to model it. Once my model was fitted, it helped me to forecast future values of the flow of direct imports in Mexico

Based on the selected results, please share at least 1 recommendation that address the problem situation.

• I first recommend to gather the data from the same periods, this caused me a lot of problems to analyze the information.

• For future inversionists I would say that the variables Educacion and Inseguridad Homicidio are important factors that asffect IED flow, so I would recommend to check on this levels first.

• A 1-unit increase in the logarithm of “Educacion” is related with an estimated increase of 2.54806 in the variable, holding other variables constant. This is statistically significant at the 0.05/5%.

• A 1-unit increase in variable “Inseguridad_Homicidio” is related with a decrease of 0.34275 in the variable, and the other variables are constant. This is also statistically significant at the 5%l.

References

TIBCO (2023, March 24) Time Series Analysis https://www.tibco.com/reference-center/what-is-time-series-analysis

A.Figueroa (2023, August 9) The Rise of Nearshoring to Mexico https://www.nuvocargo.com/en/content/blog-posts/key-cross-border-trends-the-rise-of-nearshoring-to-mexico