DavidEnriqueNieves/UkraineWarWorldEconomy
A group project for Florida Tech's MTH5324 (Statistical Modelling) project that analyzes the impact of the Russo-Ukraine war on the economy of several significant geopolitical entities.
Analyzing the Russo-Ukrainian War's Effect On The World Economy
David Nieves Acarón & Sam Sharp
MTH-5324
Dr. Nezamoddin N. Kachouie
Spring 2023
Abstract
In this project we explore the effects of the Russo-Ukrainian war on the
economies of the United States, Japan, the People's Republic of China,
and the European Union, primarily through analysis of their respective
Gross Domestic Product and national currency values. Three distinct
methods are used for our analysis being multiple regression, generalized
additive models, and autoregressive models. Through hypothesis testing
for separate multiple regression models and forecasting over post-war
data, we establish noticeable effects on the economies of these nations
from the war. Additionally, similar results can be illustrated on
relevant commodity prices associated with Russia and Ukraine.
Introduction
The analysis of the economic impact of a war is just one way of
assigning meaning to it. In this report, we are concerned with
establishing a connection between a change in economic variables for the
United States, China, the European Union, and Japan before and after the
invasion of Ukraine in February of 2022. The events of late February
2022 shocked much of the world and resulted in large scale economic
shifts. Almost immediately following the invasion, a cascade of economic
turmoil entered financial markets across the globe while certain
economies have begun to see higher inflation. Energy and food crises
became household topics and many nations enacted economic sanctions
against the Russian Federation.
Our goal is primarily to find a significant effect of the war on certain
economies using statistical tests and forecasting methods. Multiple
regression, generalized additive models, and autoregressive models are
employed to achieve these ends with promising results to be expanded on.
For multiple regression, we construct a multitude of models and then
conduct hypothesis tests on predictors to establish if there is a
significant difference in the independent variable's estimate
coefficients between the pre-war and post-war eras. Owing to their
benefit with nonlinearity, generalized additive models (GAMs) are
employed in an effort to fit models which can attempt to accurately
forecast the GDP and currency evolution under models trained under
pre-war datasets.
There is a multitude of statistical research papers analyzing the
effects of war and other conflicts on economies and related variables.
Glick and Taylor used statistical methods to measure the effects of war
on trade between warring and neutral nations, with a conclusion that the
economic welfare of such nations is significantly affected [@glick] .
Nations in Sub-Saharan Africa have been shown to have higher levels of
civil conflict when experiencing negative economic growth [@subafrica].
Researchers at Harvard University have given support to the notion that
civil wars can significantly effect economic growth, particularly with
respect to private investment [@economic_civil_war]. Furthermore and
related to our own look at GDP, a study from the European Bank for
Reconstruction and Development establishes a significant drop in GDP by
nations in a state of war and other nations not experiencing war on
their own territory. Additionally, this study shows lasting effects on
the labor force supply and capital stocks even after the affecting war
has concluded [@european_bank]. These studies not only establish these
negative relations with respect to warring nations, but also nations
which take no part in the fighting itself, as seen by African nations
not in civil conflict, or trade levels decreasing among nations not
taking part in wars. This motivates our own research into the economic
effects of the war in Ukraine on nations such as China, the United
States, and Japan. While these nations are not fighting with troops on
the ground, statistical analysis might still be able to show a
significant difference on their economies in pre-war and post-war eras.
Regarding our methods, the utilization of multiple regression is
prevalent in such related studies. Book and Ekelöf use multiple linear
regression techniques to establish the connection between the success of
small businesses and certain macroeconomic factors
[@macroeconomic_mult_linreg]. Stephen Bazen expands on the overwhelming
utility of linear regression models for labor economics, showing that
such models are extremely prevalent in an economic context
[@linear_regression_economics]. Similarly, besides the use of multiple
regression, other models will be considered due in part to the
limitations associated with regression. First, there is no dearth of GAM
related research regarding economics. Consider the study by S. Sapra
which utilized multiple GAM models on business and economic datasets
across a range of potential applications. This study expands on the
potential advantage of a GAM against a standard multiple regression
model in the case where there is an inadequate fit [@GAM_business].
Additionally, for example, the use of autoregressive, time-series models
with economic data is a well-established practice as seen in
[@time_series_models]. In particular, ARIMA models as developed by
[@ARIMA_original] are widely used in forecasting time-series data for
economics and finance [@ARIMA_forecasting], which is partially why they
were chosen for this project. Moreover, combined with the use of
exogeneous variables which change in time and also affect the response
variables has been applied to several economics and business
applications. For example, [@Thailand_ARIMAX] attempt to use ARIMAX to
model Thailand's exports to her trade partners, [@US-China-ARIMAX]
attempts to model the monthly average of Brent crude oil price with the
influence of the US-China trade war, and [@irish-civil-war-ARIMAX]
attempt to model suicide rates during and after the Irish Civil War.
In sum, we see that Multiple Regression, Autoregression, and GAMS could
be effectively utilized to measure the effects of the Russo-Ukrainian
war on the world economy.
Data
Our data is gathered from a wide variety of sources. Primarily, these
involve FRED, Eurostat (the European Union's Statistics
Directourate-General), the People's Bank of China, and the Bank of
Japan. For each nation, we constructed a dataset comprising quarterly
Gross Domestic Product (real or gross as specified further), Interest
Rates (from their respective central bank), unemployment rate,
government spending, the consumer price index (CPI), and the national
currency for each respective nation. Our dataset is on a monthly time
frame, and as such, in instances where quarterly data was gathered,
linear interpolation was used to augment the data into months. For all
data regarding currencies, only Close prices are used.
Each nation's dataset is split into a pre-war dataset and post-war
dataset for hypothesis testing and forecasting uses that will be
discussed in the methods section. For the European Union, Japan, and the
United States, the pre-war dataset consists of 121 individual months of
data ranging from January 2012 to January 2022, while the post-war
dataset consists of 14 months from February 2022 to April of 2023. The
Chinese dataset is considerably shorter, with the pre-war dataset
consisting of 47 months which ranges from August of 2018 to January of
2022, and the post-war dataset the same 14 months as the latter three.
First, for the United States, the CPI is for all consumer items for all
wage earners in the United States as listed by the OECD on a quarterly
basis. The interest rate data is the Federal Funds Rate given by the
Federal Reserve of the United States. The government spending data is as
percentage of the deficit (or surplus) relative to the gross GDP of the
United States. The GDP is gross, not seasonally adjusted, given on a
quarterly basis. The unemployment rate is a percentage representing the
unemployed percentage of the available labor force. The currency dollar
is the U.S. Dollar Index, which is a relative metric which gauges the
value of the U.S. dollar relative to European Union, Swiss Franc,
Japanese Yen, Canadian Dollar, British Pound, and Swedish Krona.
For the European Union's CPI, all items were considered for all
countries in the Euro area (19 countries in total) as seen in our
accompanying source. The interest rate data for the European Union is
the European Central Bank's Main Refinancing Operation Rate under Fixed
Rate tenders. This was chosen as an analogue to the Federal Reserve's
Federal Funds Rate. For government spending, the data used involved the
19 country area as seen in the accompanying Eurostat source. Its units
are in percentages and they are listed from 2013 to 2022 in a yearly
basis. Similarly for unemployment rates, the 19 country zone
unemployment in units of percentages was used. The granularity of this
data is in months, ranging from 1990 to January of 2023. Finally, the
Euro's performance was obtained from Yahoo Finance's Python API using
the ticker symbol of "EURUSD=X", with it being measured relative to
the U.S. dollar.
The PRC's data was the most burdensome to obtain as many of the data is
listed in a yearly basis. The CPI is in units in 2015 indices in a
quarterly granularity, with the dates ranging from 1993 to 2022 given as
under all items by the OECD. The government spending is a percentage of
the deficit relative to China's GDP that quarter. The GDP is the Real
GDP (relative to 2017 U.S. dollars) given yearly. The interest rate used
is the Chinese 1 year Loan Prime Rate from the People's Bank of China.
The interest rates were obtained from an intermediary source which in
turn gets the data from our attached primary source. They are in units
of percentages and are in yearly granularities. The unemployment rate is
also in percentages in a yearly granularity measured as the percentage
of the labor force which is unemployed. Similarly, the currency data
corresponds to the USD/CNY pairing with symbol "CNY=X" from Yahoo
Finance.
The CPI for Japan is with respect to All Items of 2015 indices, with a
quarterly granularity from 1960 to the first quarter of 2022. The
interest rate is in the form of monthly units of percentages, with
ranges from 1960 to February of 2023. This interest rate is the
immediate 24 hour lending rate set by the Bank of Japan. For government
spending, this is taken as a percent of government expenditure relative
to GDP in yearly time ranges from 1970 to 2021. The GDP is quarterly,
tied to the value of the Yen in 2015. The unemployment rate for Japan is
a percentage of the unemployed populace ages 15 to 64, listed quarterly.
Finally, the currency is the Japanese Yen relative to the Dollar, taken
as the value at the end of each month.
The commodity data is the daily closing price for the following futures:
Natural Gas (NY Mercantile), Wheat(CBOT Chicago), Crude Oil (NY
Mercantile), and Soybean Oil (CBOT Chicago). Prices are valued in
Dollars.
Please see Tables 1-5 in the supplementary report file for the sources
for each respective data entry in the References section.
A combination of R scripts and Python scripts were used to aggregate the
data. The use of an advanced text editor known as Vim was also of great
value for quickly editing CSV files. The greatest issue we had was in
aggregating data with different date formats. Some examples of these
scripts used for this purpose include main.py commodi̇pynb, and
change_date_format.py.
Methods
We begin with multiple regression. Various multiple regression models
were utilized, with two separate dependent variables studied. The two
dependent variables used for our multiple regression models were each
nation's monthly GDP and their respective currencies. Primarily, our
regression models encompass two separate forms. The first is the
standard regression with a dependent variable and multiple independent
variables. The second is a difference model, which takes the same
structure as the standard regression model with the exception that every
variable is now recomputed as the difference between the two most recent
entries. As for deciding which independent variables to use for each
nation's respective dataset, correlation matrices were used for both
standard and difference models. An example of these correlation matrices
can be seen in Figure 1 of the supplementary document. Furthermore, one
extra multiple regression model was utilized, which is the case of
Robust Linear Models (RLMs), using Huber loss and M-estimators. Iterated
reweighted least squares is used to find an M-estimator, which is used
to better handle the effect of outliers on regression, which in turn can
help one overcome violations of the assumptions of linear regression.
For further information on the theory of robust regression, see
[@RobustRegression] and [@huber].
The main method as for ascertaining an effect post-invasion on the
nations economies comes in the form of testing whether there is a
significant difference in the regression slopes on our pre-war and
post-war models. This comes in the form of the following hypothesis
test:
Where
independent variable on the pre-war model and
respective estimate coefficient for the independent variable on the
post-war model. To test this hypothesis, we calculate the test-statistic
as:
Where
respectively. In the case of,
We are able to reject the null hypothesis and establish some statistical
difference between the way the independent variable has affected the
response variable between the pre-war and post-war eras. For this
research, we use a 95$%$ confidence interval. These hypothesis tests
are only conducted if a certain multiple regression model returns
independent variables in the regression summary which are both
statistically significant. In this case, the hypothesis test is
conducted. The equations (1) and (2) were introduced and established as
good practice by [@correct_stats], who denote this practice as
well-defined and effective in a criminology journal.
Additionally, we utilize GAMs for further efforts of forecasting. Tables
3 through 6 show each GAM model and the independent variables it used.
Note that we employ two separate methods for these GAMS, one being
Generalized Cross Validation (GCV) and the other Restricted Maximum
Likelihood (REML). While GCV is the default designation for GAMs, we
have chose to also utilize REML methods based on research in the
literature suggesting that GCV methods can be prone to under-smoothing
[@GAM_wood]. Every independent variable is made a smooth term using thin
plate splines. In the post-war GAM models, knots of three units are used
to ensure convergence.
For the autoregressive models, some analysis of the data was performed
to determine what the model parameters,
This was done by looking at the partial autocorrelation function, the
Dickey-Fuller test [@Dickey-Fuller], and the autocorrelation function,
which can help to determine the coefficients for
respectively. The coefficients for
significant partial autocorrelation lag value, regardless of whether it
lied inside or outside of the confidence intervals. the autocorrelation
lag term was chosen by taking the last lag for which the term was
significant (i.e. outside of the confidence interval). With regards to
ARIMAX, the exogeneous variables were chosen by using the indicators
which were previously shown to be significant by the earlier tests. For
the
performing differencing on the response data using the diff function
in R until the p-value of the test was found to be less than 0.01. A
forecast of the response was performed by using the forecast function
in R. This was then plotted against the points that reflected the true
response values at the times after the war started in order to get a
sense of how different the actual response values are when compared to
the forecasted response values. This process was repeated for both the
country GDP data along with the associated exogeneous variables
indicated in each of the accompanying plots as well as the commodity
data. To get a sense of how different the post-war and pre-war
situations are and thus to possibly conclude that there is a significant
difference, the use of the ARIMA & ARIMAX confidence intervals can be
employed to see which of the predicted points lie outside of the 95%
confidence intervals (colored in light grey in the plots) of the ARIMA
and ARIMAX forecasts.
Results
Table 1 lists each respective model for each nation's dataset and the
independent variables used in the regression as dictated by the
correlation matrices, as well as the pre-war and post-war respective
models Adjusted R-squared value. Table 2 lists the independent variables
which were significant in both pre-war and post-war models which then
subsequently were able to reject the null hypothesis. Table 2 also lists
each rejected predictors pre-war and post-war estimate coefficients, so
one can see the change in how these variables effect the response from
pre-war to post-war eras. The ARIMA forecasts superimposed over the
post-war data for each commodity appears in Figure 1, where we can see
the ARIMA models struggling to accurately forecast the events of the
war. In Figures 2 and 3, the ARIMAX forecast is displayed for each
nation over the post-war period. Figures 4 through 10 display each GAM
forecast using GCV and REML methods for GDP and national currencies as
responses. Correspondingly, Tables 3 through 6 show each GAM model with
their respective Deviance Explained as a percentage.
Discussion and Conclusion
To begin, we find many simultaneous significant independent variables in
multiple models across each nation which are then able to reject our
null hypothesis (1), as seen in Table 2. Chiefly among these, we find
the largest prevalence of rejected hypothesis predictors in that of
Japan and the European Union, which might indicate these two have felt
the largest impact since the war. The United States sees patterns by
rejecting GDP and CPI in multiple models, where we interestingly see the
effect of CPI on the Dollar transitioning from a negative coefficient to
a positive one in pre-war and post-war eras. Among the European Union,
we see particular trends in rejecting the Euro, CPI, Government
Spending, and Interest Rates. Similarly Japan sees trends in the
rejections of Government Spending, Unemployment Rate, and CPI across
almost all models. Finally, the PRC has the least significant results,
with only two predictors rejected among all six models, these being
Government Spending and Interest Rates.
Comparing broadly among all datasets, we see the effect of CPI on GDP
significantly changing in Japan, the United States, and the European
Union. The change in regression coefficients for CPI on GDP in many of
these cases is that of CPI increases in the post-war era being less
positively correlated to a nation's rising GDP, which might imply the
effects of the war have led to an increase in inflation while
simultaneously not increasing the GDP by a large margin, as one would
expect with such currency inflation. This could imply we are beginning
to see the entry of a stagflationary cycle in the nations where we note
this phenomenon- the USA, the European Union, and Japan. Another, less
alarming, angle to see this could be a significant lag in the GDP growth
catching up to inflationary trends.
Another significant trend observed in the three highly affected datasets
(the EU, US, and Japan), is a broad trend of the GDP's effect on the
national currency being statistically different in the pre-war and
post-war eras. In Japan and the European Union, every instance of GDP
affecting currency results in a transition to a higher positive effect
on the currency itself. Since our Euro and Yen data is gauged in
strength relative to the dollar, this could imply that these national
currencies have gained in strength with their respective GDP while the
value of the Dollar has weakened. Further supporting this, we see an
opposite trend in the USA, with the GDP transitioning from a positive
effect on the dollar to a negative effect.
With respect to Government spending, the economies of the European Union
and Japan both see a similar transition from higher government spending
leading to a positive effect (or lesser negative effect) on GDP to a
highly negative effect in the post-war era. One possible explanation of
this is these two respective entities are responding to the invasion by
increasing their spending towards military aims, which can be seen from
the recent efforts to re-militarize Japan [@japan_war] and European
nations such as Poland reacting to the invasion by increasing the
capacity of their armed forces [@Poland].
Japan is the only nation which finds statistically significant
differences with respect to the unemployment rate's effect on GDP. Each
instance of rejection results in a shift from a negative effect to a
positive effect or a less negative effect on GDP. One inference of this
result could be that since unemployment rate has been relatively stable
in the post-war era, any raise in GDP could be cancelling out the
negative properties of a higher unemployment rate seen in the pre-war
regressions.
Curiously, we see few instances in any model across any nation where we
can find a statistical difference with interest rates as a predictor.
There are a few explanations for this, one being that many models were
unable to use interest rates as an independent variable due to
multicollinearity issues. In the cases where we do have a rejected
hypothesis (Chinese GDP and EU Euro), we see the same result with an
increase in interest rates affecting GDP less negatively in the post-war
era. Here, we can summarize that interest rate increases in the European
Union have less negatively effected the EU economy as previously seen
with rate rises. The cause of this is not known at the time and should
be studied further.
Additionally, the multiple regression models had relatively strong
adjusted R-squared values. Across the board, the non-robust models have
adjusted R-squared values ranging from around 0.4 to 0.98 across the
pre-war and post-war models. The difference models have less strong
adjusted R-squared values which might imply a faulty employment of such
methods. Additional work can be down to analyze further if the
difference models are properly implemented.
Regarding the GAM models, forecasting accuracy varies across each nation
and the respective dependent variable. Overall, we see very similar
forecasting results between GCV and REML methods with the exception of
European Union forecasting results on GDP.
The United States shows very inaccurate forecasting results with respect
to GDP under both methods, while Dollar forecasting results remain close
to the fitted model and well in the confidence intervals. These
inaccurate GDP forecasts might show that the post-war American GDP is
exceeding expectations under less favorable macroeconomic conditions,
while the dollar is relatively stable.
European Union forecasts remain in the confidence intervals under the
GCV method and straddle the bounds of the confidence intervals for the
REML method. The reason for the inverted fit discrepancy seen in Figure
5 is unknown and deserves more analysis. The Euro is forecasted
accurately by both models as seen in Figure 6. Similarly to the United
States, one might infer that the Euro has remained stable since the
invasion.
Both GDP and Yen forecasts are inaccurate. As the Japanese GDP has
stayed essentially constant in the post-war era as seen in Figure 7
while other macroeconomic variables changed, it is reasonable to assume
that the fitted forecast would be error prone. This is further supported
by the previous acknowledgement of Japan having the highest rate of
rejected predictors from Table 2. The results in Figure 8 implies the
Yen is performing stronger than expected in light of the change in
economic variables.
The forecasting results for Chinese GDP are accurate while the
forecasting for the Renminbi has significant errors. Figure 10 shows
that the fitted models expect a poorer performance of the Renminbi while
in reality it has become more valuable.
Tables 3 through 6 show us the Deviance Explained from each GAM model,
with values mostly very high between 92 percent and 98.8 percent for the
European Union, Japan, and the United States. China shows less Deviance
Explained with respect to the currency response models. This is
suspected to be from the lack of data for China compared to the other
nations.
For clarification, the $n$th "lag" in an autocorrelation plot refers to
the amount of correlation that the $n$th term has to the current term in
the time series. The ARIMAX results for the country GDP data were
varied. In many cases, the partial autocorrelation functions of the GDP
for the countries had its most significant lag above the 8 lag. In the
case of the United States and the EU, this highly significant lag occurs
at around the 13 mark. In the case of Japan and the PRC, this occurs at
around the 8 or 9 lag mark. As this analysis was done in quarters, it
could be said that at least for the United States and the European
Union, this could be a byproduct of the COVID-19 epidemic's initial
economic fallout around 13 quarters ago (Q1 of 2020). Besides that, none
of the other lag terms were significant enough to lie outside of the 95%
confidence intervals highlighted in blue. The partial autocorrelation
functions paint a different story, as there are terms that are the most
significant as far as the 9th lag mark. These marks diminish steadily in
size, with the first lag mark having the highest autocorrelation and the
successive lag marks having less autocorrelation until lying within the
marks of the confidence interval. With the European Union's
autocorrelation function, the lags are a bit less significant earlier
on, with the last significant lag being located at the 6th mark.
This could perhaps be interpreted as there being less influence from
previous states in the economy. To speculate as to why, it could be
theorized that this could have to do with its relatively smaller
economic size as opposed to the United State's economy. A similar effect
occurs when comparing Japan and the PRC's economy. No stationarity was
obtained by performing the Dickey-Fuller test with the different
countries' GDP data. This likely reflects the seasonal nature of
economies. For reference, a stationary time-series is one that has a
constant mean, variance, and autocorrelation [@stationarity]. By simple
inference, it is easy to see that most if not all economies do not
exhibit stationarity. For that reason, the
how many nonseasonal differences are required for stationarity. In the
case of Japan, the United States, and Europe, a
necessary, whereas a
a differencing term is necessary for avoiding seasonality, then this
implies that data which requires a higher
nonseasonal. In turn, this implies that the PRC's GDP data is less
seasonal. This could be due to a number of reasons, some involving
economic policies aimed at maintaining its high growth rate. However,
when compared to the
that perhaps the PRC's GDP conditions are more stable than those of the
other countries.
The results pertaining to the commodities offer a clearer picture. The
time series data for all the commodities had a
could indicate that these prices are less seasonal than the GDP data
found above. The autocorrelation terms are commonly significant from the
first term all the way to the 25th term, and it's likely that even more
terms are significant. Given that the lag terms are in units of days,
this likely reflects the fact that for a single month, the price of a
commodity is highly related to its price at any other point in the past
month. Another observation is that the partial autocorrelation terms for
all the commodities are sparsely scattered, since virtually none of them
rise above the significance level of 95%. This suggests that
autocorrelation is the main factor that affects current commodity
futures prices, and not partial autocorrelation. As a result, very few
of the attempted models utilized partial autocorrelation.
For the ARIMA results regarding commodities, the results seem to
indicate patterns that diverge from what is expected from the model.
Technically, the patterns can be explained by the 95% and 80% confidence
intervals of the ARIMA models, but overall, none of the observed
patterns follow what the model predicts. This is particularly egregious
with the wheat example, which was critically affected by the onset of
the war and proceeded to diverge from the general trend by first
undergoing a steep rise followed by a steep fall and a modest falloff.
Some more subdued examples can be found in the Soybean Oil futures and
Natural Gas futures.
Overall, we have established many possible effects on the economies the
United States, European Union, China, and Japan as a result of the
Russo-Ukrainian War through multiple regression and the forecasting
methods of GAMs and autoregressive models. Additionally, while the
ARIMAX results for the countries offer mixed results, with Europe
showing the most drastic change from the model's expectations and
Japan's results being expected, the results of ARIMA modelling with
regards to commidites offers a distinct change that occurs at the onset
of the war. This in turn yields the clearest picture among all the
autoregressive model results and clearly shows a change from the prewar
conditions. Further work can expand on improved datasets, involving more
nations, using more advanced regression techniques as well as utilizing
neural network models to advance similar results.
While there is no absolute conclusion of a negative downturn across the
global economy, we present significant results to illustrate that
economic variables have shifted in light of a large scale war coming to
Europe.
References
9
Paternoster, R., Brame, R., Mazerolle, P., & Piquero, A. (1998). Using
the correct statistical test for the equality of regression
coefficients. Criminology, 36(4), 859-866.
Sapra, S. K. (2013). Generalized additive models in business and
economics. International Journal of Advanced Statistics and Probability,
1(3), 64-81.
Miguel, E., Satyanath, S., & Sergenti, E. (2004). Economic Shocks and
Civil Conflict: An Instrumental Variables Approach. Journal of Political
Economy, 112(4), 725--753. https://doi.org/10.1086/421174
Book, E., & Ekelöf, L. (2019). A Multiple Linear Regression Model To
Assess The Effects of Macroeconomic Factors On Small and Medium-Sized
Enterprises.
Imai, K., & Weinstein, J. M. (2000). Measuring the economic impact of
civil war. CID Working Paper Series.
Bazen, S. (2011). The use of linear regression in labour economics.
Econometric Methods for Labour Economics, 4--33.
https://doi.org/10.1093/acprof:oso/9780199576791.003.0002
A. Colin Cameron and Pravin K. Trivedi (2013), Regression Analysis of
Count Data, 2nd edition, Econometric Society Monograph No.53, Cambridge
University Press, 1998 (566 pages.)
Gelman A, Hill J., and Vehtari A. (2020) Regression and Other Stories,
Cambridge University Press
Smelser, N. J., & Baltes, P. B. (2001, November). Time Series: Economic
forecasting - harvard university. Retrieved April 29, 2023, from
https://scholar.harvard.edu/files/stock/files/time\_series\_economic\_forecasting.pdf
Siami-Namini, S., & Siami Namin, A. (n.d.). Forecasting economics and
financial time series: Arima vs. LSTM. Retrieved April 29, 2023, from
https://ui.adsabs.harvard.edu/abs/2018arXiv180306386S/abstract
Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time
series analysis: forecasting and control. John Wiley & Sons.
Kongcharoen, C., & Kruangpradit, T. (2013, June). Autoregressive
integrated moving average with explanatory variable (ARIMAX) model for
Thailand export. In 33rd International Symposium on Forecasting, South
Korea (pp. 1-8).
Rahmayanti, I., Andreas, C., & Ulyah, S. (2021). Does US-China trade war
affect the Brent crude oil price? An ARIMAX forecasting approach. AIP
Conference Proceedings, 2329(1).
Mugtaba Osman, Andrew Parnell, & MacDara McCauley (2018). Effect of the
Irish Civil War 1922-1923on suicide rates in Ireland: a
retrospectiveinvestigation of the archives of the registrar general for
Saorstat Éireann. Epidemiology Biostatistics and Public Health, 15(3),
e12920.
Wheat in Ukraine. (n.d.). Retrieved April 29, 2023, from
https://oec.world/en/profile/bilateral-product/wheat/reporter/ukr
S. E. Said and D. A. Dickey (1984): Testing for Unit Roots in
Autoregressive-Moving Average Models of Unknown Order. Biometrika 71,
599--607.
Fuqua School of Business. (n.d.). Stationarity and differencing of time
series data. https://people.duke.edu/ rnau/411diff.htm
Miguel, E., Satyanath, S., & Sergenti, E. (2004). Economic shocks and
civil conflict: An instrumental variables approach. Journal of political
Economy, 112(4), 725-753.
Chupilkin, M., & Koczan, Z. (2022). The Economic Consequences of War:
Estimates Using Synthetic Controls. European Bank for Reconstruction and
Development.
Glick, R., & Taylor, A. M. (2010). Collateral damage: Trade disruption
and the economic impact of war. The Review of Economics and Statistics,
92(1), 102-127.
Osborn, K. (2022, January 18). The Russian threat is behind Poland's
F-35 purchase. Retrieved April 29, 2023, from
https://nationalinterest.org/blog/buzz/russian-threat-behind-polands-f-35-purchase-199587
Li, R. (n.d.). The Remilitarization of Japan: An Uncertain Future.
Retrieved April 29, 2023, from
https://cs.wellesley.edu/ lianka110/beta/article1.html
Wood, S. N. (2006). Generalized Additive Models: An Introduction with R.
Chapman and Hall/CRC.
Ruckstuhl, A. (2016). Robust Fitting of Parametric Models Based on
M-Estimation.
P. J. Huber (1981) Robust Statistics. Wiley.