(Tiểu luận) forecasting pepsico’s revenue from q3 2023 to q4 2024

In pursuit of thisobjective, various forecasting methods were employed, including the Nạve adjustedmethod, Holt-Winter's exponential smoothing, time decomposition, and the ARIMAAutoRegre

FOREIGN TRADE UNIVERSITY FACULTY OF INTERNATIONAL ECONOMICS

-*** -FORECASTS IN ECONOMICS AND BUSINESS REPORT

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FORECASTING PEPSICO’S REVENUE FROM Q3 2023 TO Q4 2024

Hanoi, October 2023

INDIVIDUAL ASSESSMENT

No Name Student ID Contribution Bonus point Signature

1 Bùi Trung Đức 2113450009 24%

2 Chu Nam Khánh 2011450202 24%

3 Vũ Trần Khánh Linh 2113450020 28% +

4 Nguyễn Nam Thành 2013450421 24%

TABLE OF CONTENT

ABSTRACT 1

INTRODUCTION 2

A Problem Formulation 2

B Literature Review 4

C Forecasting Objectives 6

D Forecasting Series 7

SECTION 1: EXPLORING DATA PATTERNS 8

1.1 Data collection 8

1.2 Data nature 8

1.3 Data patterns analyzing 9

SECTION 2: FORECASTING TECHNIQUES SELECTION 13

2.1 Naive model adjusted for trend and seasonality 13

2.2 Holt-Winter’s exponential smoothing model 14

2.2.1 For additive model 14

2.2.2 For the multiplicative model 15

2.3 Time series decomposition (Seasonal Adjustment) 16

2.3.1 For additive model 16

2.3.2 For multiplicative model 17

2.4 ARIMA model 19

2.4.1 Definition 19

2.4.2 Model 20

2.4.3 Process 22

SECTION 3: FORECASTING RESULTS 23

3.1 Nạve model adjusted for trend and seasonality method 23

3.2 Holt-Winters exponential smoothing method 25

3.3 Time series decomposition method 27

3.4 ARIMA model 35

3.5 Forecast evaluation 42

3.6 Forecast for future period 43

CONCLUSION 45

REFERENCES 46

This report delves into the task of forecasting the revenues of PepsiCo Inc for theperiod spanning from the third quarter of 2023 to the fourth quarter of 2024 Accuraterevenue forecasting is of paramount importance for both internal decision-making andexternal stakeholders' assessment of a company's financial performance In pursuit of thisobjective, various forecasting methods were employed, including the Nạve adjustedmethod, Holt-Winter's exponential smoothing, time decomposition, and the ARIMA(AutoRegressive Integrated Moving Average) model These methodologies were appliedusing advanced statistical tools and software, facilitating a rigorous analysis of historicalrevenue data and trends

The findings of this study reveal unique insights into the anticipated trajectory ofPepsiCo's revenues during the specified timeframe Additionally, the report assesses theforecast accuracy of each method through metrics such as Mean Absolute PercentageError (MAPE) Preliminary results suggest that certain forecasting techniques outperformothers, demonstrating their potential to provide reliable revenue predictions Theimplications of these forecasts will be discussed in detail, shedding light on the factorsinfluencing PepsiCo's revenue performance in the upcoming quarters and theirsignificance for stakeholders and decision-makers

● Key Terms:

ARIMA: AutoRegressive Integrated Moving Average

MAPE: Mean Absolute Percentage Error

Operating in more than 200 countries and territories, PepsiCo's reach extends toevery corner of the globe, making it an integral part of daily life for countless individuals.The company's enduring success can be attributed to its unwavering dedication todelivering quality products, fostering innovation, and embracing responsible businesspractices As we delve into forecasting PepsiCo's revenues from the third quarter of 2023

to the fourth quarter of 2024, it is imperative to understand the dynamic nature of thisindustry giant and the multitude of factors that influence its financial performance Thisreport aims to provide a comprehensive analysis of PepsiCo's revenue forecasts, utilizing

a range of forecasting methodologies to shed light on the company's anticipated financialtrajectory in the upcoming quarters

A Problem Formulation

PepsiCo Inc., a global juggernaut in the food and beverage industry, boasts a vastand diverse product portfolio that resonates with consumers worldwide Founded on themerger of Pepsi-Cola and Frito-Lay in 1965, the company has grown to encompass anarray of beloved brands that range from carbonated soft drinks and savory snacks tonutritious beverages and beyond As of our knowledge cutoff date in September 2021,PepsiCo's reach extended to over 200 countries and territories, firmly establishing it as apowerhouse in the consumer goods sector

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PDP template 1International

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Đại số tuyến tính Thầy Đặng Lê Quan…

-This report embarks on a crucial mission: forecasting PepsiCo's revenues from thethird quarter of 2023 to the fourth quarter of 2024 Accurate revenue forecasting holdsimmense significance for both internal stakeholders within PepsiCo's strategic planningteams and external actors, such as investors, market analysts, and observers keen ondeciphering the financial health of the company Several intricacies underpin thisforecasting endeavor:

● Market Dynamics: The food and beverage industry is a dynamic arena, marked byconstantly shifting consumer preferences, economic ebbs and flows, and globalevents Accurately predicting revenue amidst this ever-changing landscape is aformidable task

● Diverse Product Mix: PepsiCo's extensive product mix encompasses a broadspectrum of categories, from traditional soft drinks and snacks to health-focusedalternatives Each category may react differently to market forces, necessitating anuanced forecasting approach

● Global Footprint: Operating across a vast global footprint, PepsiCo's revenues areinfluenced by a multitude of geographical markets, each with its own uniquedynamics Understanding these market nuances is pivotal to precise revenueforecasting

● Competitive Landscape: The food and beverage industry is fiercely competitive,characterized by rapid product innovation and fluctuating consumer tastes Adeptrevenue forecasting can confer a competitive edge by enabling the company toswiftly adapt to market shifts

● Economic Influences: Macroeconomic variables, encompassing inflation rates,currency exchange fluctuations, and GDP growth, have substantial repercussions

on PepsiCo's revenues Accurately projecting the evolution of these factors is alinchpin of accurate forecasting

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InternationalBusiness… NoneReport - Team 04 - KDOE305

InternationalBusiness… None

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In light of these intricacies, the core problem addressed in this report revolvesaround devising a robust and dependable methodology for forecasting PepsiCo'srevenues An array of forecasting techniques, including the Nạve adjusted method, Holt-Winter's exponential smoothing, time decomposition, and the ARIMA model, will beevaluated for their forecast accuracy.

Ultimately, this report seeks to equip PepsiCo and its stakeholders with actionablerevenue forecasts that can inform strategic choices, resource allocation, and riskmitigation strategies, ensuring the company's continued success in a marketplace marked

by complexity and continuous evolution The forecasting insights derived here hold thepotential to guide investment decisions, industry analysis, and strategic planning,contributing to PepsiCo's enduring stature as a global industry leader

B Literature Review

Forecasting financial metrics, such as revenues, is a critical endeavor in modernbusiness, essential for strategic planning, investment decisions, and overall corporateperformance assessment In the context of forecasting PepsiCo Inc.'s revenues, acomprehensive literature review reveals a rich landscape of methodologies and insightsapplied to similar forecasting tasks within the financial and consumer goods sectors

1 Forecasting Methodologies

The literature is replete with various forecasting methodologies, each offering itsunique approach to predicting financial performance These methodologies can bebroadly categorized into quantitative and qualitative techniques:

● Quantitative Methods: Quantitative forecasting techniques, like time seriesanalysis, have been extensively employed in revenue forecasting Time seriesmodels, including exponential smoothing, moving averages, and autoregressiveintegrated moving average (ARIMA), have proven effective in capturing historicaltrends and seasonality in financial data Researchers often adapt these methods to

specific industries and datasets, tailoring them to the unique characteristics of thecompany under examination.

● Qualitative Methods: Qualitative forecasting techniques, such as expert judgmentand market research, provide valuable qualitative insights that quantitative modelsmay overlook Surveys, interviews, and focus groups can offer qualitative data thatcomplements quantitative analysis, especially in industries where consumerpreferences and market sentiment play a significant role

● Supply Chain Dynamics: Fluctuations in the supply chain, driven by factors likecommodity prices, transportation costs, and supply disruptions, have a directimpact on revenue Forecasters need to account for these variables

● Marketing and Promotion: Effective marketing campaigns and promotions cansignificantly impact sales Incorporating marketing spend and promotionalactivities into forecasting models is essential for an accurate prediction ofrevenues

3 Data Sources and Availability

The availability and quality of data are paramount in revenue forecasting.Researchers and analysts often grapple with issues related to data granularity,completeness, and accuracy Additionally, the integration of external data sources, such aseconomic indicators and market research, can enhance the precision of revenue forecasts

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4 Forecast Evaluation Metrics

To assess the reliability of forecasting models, researchers commonly employmetrics like Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), andRoot Mean Square Error (RMSE) These metrics help quantify the accuracy of forecastsand allow for comparisons between different forecasting approaches

5 The Role of Advanced Analytics and Machine Learning

Recent advancements in data analytics and machine learning have ushered ininnovative approaches to revenue forecasting These techniques can handle vast datasets,identify complex patterns, and adapt in real-time to changing market dynamics.Incorporating machine learning algorithms, such as neural networks and ensemblemethods, has become increasingly common in financial forecasting

6 Economic and Market Factors

Global economic conditions, including inflation rates, currency exchange rates,and GDP growth, profoundly influence revenue forecasts Researchers often integrateeconomic indicators into forecasting models to capture macroeconomic effects accurately

In summary, forecasting PepsiCo Inc.'s revenues is a multifaceted task thatrequires a thoughtful integration of quantitative and qualitative methods, industry-specificconsiderations, data quality, and an understanding of external factors The literatureunderscores the importance of a comprehensive approach, drawing insights from diversesources and methodologies to enhance the accuracy of revenue forecasts This reviewforms the foundation for the subsequent analysis and methodology selection in thisreport, aimed at providing a robust revenue forecast for PepsiCo

C Forecasting Objectives

The primary objective of forecasting in the context of PepsiCo Inc.'s revenues is toprovide decision-makers with accurate, timely, and actionable insights into the company's

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future financial performance This entails predicting revenue levels with a high degree ofprecision, enabling informed strategic decisions, resource allocation, and riskmanagement Additionally, forecasting aims to enhance investor confidence and facilitatetransparent communication with stakeholders, contributing to the company's sustainedgrowth and profitability.

Furthermore, forecasting objectives extend beyond the corporate realm, serving as

a vital tool for market analysts, policymakers, and economic observers Accurate revenueforecasts for PepsiCo can inform broader economic assessments, helping policymakersmake informed decisions on matters like interest rates and fiscal policies, ultimatelyinfluencing the wider economic landscape

D Forecasting Series

In the context of revenue forecasting for PepsiCo, the forecasting series representsthe historical and future revenue data that forms the basis of the forecasting analysis Thisseries typically includes quarterly or annual revenue figures spanning a specified period,

in this case, from Quarter 1 2010 to Quarter 4 2024 The forecasting series serves as thefoundational dataset upon which various forecasting methodologies are applied,encompassing quantitative and qualitative data related to PepsiCo's revenue streams.The forecasting series is characterized by historical revenue trends, seasonality,and potentially influential external factors, such as economic indicators and marketdynamics Accurate modeling and analysis of this series are essential to develop reliablerevenue forecasts that can guide strategic decisions and provide valuable insights tostakeholders, investors, and policymakers

SECTION 1: EXPLORING DATA PATTERNS

1.1 Data collection

The revenue of PepsiCo was extracted from the website Macrotrends Utilizingsecondary data sources to obtain a comprehensive and reliable dataset is a crucial factor

in the feasibility of quantitative research studies

In our research, we are employing quarterly observations ranging from January

2010 to June 2023 by scraping data from reputable information sites The primaryobjective of the research is to forecast the trend of PepsiCo’s revenue from Quarter 1

2010 to Quarter 4 2024 Given a dataset of 54 observations, this constitutes a term forecast However, it is important to acknowledge that there may be limitations andexceptions associated with using secondary data, which could potentially lead tovariations in the forecasted results

Table 1.1 Descriptive data

Source: Author’s team compiled from EVIEWSBased on a descriptive statistical table, we can imply that the average revenue ofPepsiCo over a 14-year period is about 17,000 million $ The maximum revenue is

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approximately 28,000 million $, in the third quarter of 2022, was three times as large asthe minimum revenue in the first quarter of 2010 (9,000 million $) This implies theimpressive growth of PepsiCo’s revenue The standard deviation is 3.5265, indicating thatobservations vary a lot around the mean.

1.3 Data patterns analyzing

1.3.1 Graph

Figure 1.1 Line graph of Pepsico’ revenue from Jan 2010 to Jul 2023

Source: Author’s team compiled from EVIEWSFrom the graph, we can see that the series has an increasing trend over periods.Moreover, the amplitude of fluctuations has small changes with the trend level so theadditive forecasting model will suit best with the series

1.3.2 Seasonality testing

Source: Author’s team compiled from EVIEWS

On the second graph, the red lines represent mean values for each season Themore difference in these lines’ levels, the more obviously the seasonal component reveals

in the series We can see little difference between the red lines’ levels, hence the data hasseasonality To be more reliable, we will use the Kruskal-Wallis test to claim thestatement with hypotheses:

Kruskal–Wallis Test:

H0: No seasonal factor (distribution of Si is the same in all seasons)

H1: There is a seasonal factor (the distribution of Si is different in different seasons)

Command:

genr cma = @movavc(y,4)

genr sim = y - cma

genr quarter = @quarter

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Adj Med Chi-square 3 32.83333 0

Figure 1.2 Test for Pepsico’ revenue series

Source: Author’s team compiled from EVIEWSWith a given significant level a = 0.05, we see that P-value = 0.0000 < a

1.3.3 Correlogram

Source: Author’s team compiled from EVIEWSFrom the figure, we can imply that the data set has both trend and seasonalcomponents Therefore, it is advised to separate seasonal components before forecastingfor the better result

In conclusion, the data that we compiled has an increasing trend and seasonality Itdoes not have stationarity; however, its 2nd differences do Therefore, some suitableforecasting models will be used: naive model adjusted for trend and seasonality, Holt-Winters method, time decomposition model and ARIMA model

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SECTION 2: FORECASTING TECHNIQUES SELECTION

In reality, there are numerous models that can be used for forecasting, such as theNaive model, ARIMA model, VAR model, and so on However, after an extensiveexploration of the data patterns and evaluation of the data characteristics, the authorsbelieve that the most suitable methods for forecasting this data series are the Naive modeladjusted for trend and seasonality, Holt-Winter’s exponential smoothing model, Timeseries decomposition, ARIMA model

2.1 Naive model adjusted for trend and seasonality

The Naive model, when adjusted for both trend and seasonality, incorporates thelong-term pattern and recurring fluctuations in the data to improve its forecastingaccuracy Trend refers to the long-term direction or movement in the data, whileseasonality represents regular fluctuations that occur at fixed intervals Considering thesefactors, the model can capture the inherent patterns and variations, leading to improvedforecasting results This adjustment acknowledges the significance of trend andseasonality in understanding and predicting the behavior of the data series

When the series has trend and seasonality components, use the Naive forecastadjusted for both of them:

Or:

Where:

- : the actual value at time t

- : the forecast made at time t for time (t + 1)

- s: the number of seasons in a year

+ for quarterly data, = 4s

+ for monthly data, e4 V = 12s

2.2 Holt-Winter’s exponential smoothing model

Holt-Winter’s method extends Holt's method to allow forecasting of data with bothtrend and seasonality Holt-Winter’s exponential smoothing method consists of four mainsteps and is represented by four general equations, depending on the characteristics of themodel generated from the data series

2.2.1 For additive model

The seasonal pattern repeats yearly with increasing or decreasing magnitude

● Step 1: Calculate the exponential smoothed value of the series at time t to estimatethe level at time t

● Step 2: Estimate the trend component (slope) at time t

● Step 3: Estimate the seasonal component at time t

● Step 4: h-period ahead forecasted value

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2.2.2 For the multiplicative model

The seasonal pattern repeats yearly with almost unchanged magnitude

● Step 1: Calculate the exponential smoothed value of the series at time t to estimate

of the level at time t

● Step 2: Estimate trend component (slope) at time t

● Step 3: Estimate seasonal component at time t

● Step 4: h-period ahead forecasted value

In which:

- : the actual value at time t

- : the actual exponential smoothing value at time t

- : the estimated trend value at time t

- : estimate of the seasonal component

- s: the number of seasons in a year

- : estimated seasonal component for the period to be forecasted

+ i = n + h - s (h < s)

+ i = n + h - 2s (h > s)

- : respectively represent the exponential smoothing coefficients, the estimated trendsmoothing coefficient, and the estimated seasonal smoothing coefficient

2.3 Time series decomposition (Seasonal Adjustment)

A seasonal adjustment is a statistical technique designed to even out periodicswings in statistics or movements in supply and demand related to changing seasons.Seasonal adjustments provide a clearer view of nonseasonal trends and cyclical data thatwould otherwise be overshadowed by the seasonal differences This adjustment allowseconomists and statisticians to better understand the underlying, base trends in a giventime series

2.3.1 For additive model

The components of the time series are independent of each other

● Step 1: Data identification (additive model)

● Step 2: Separating the seasonal factor - seasonality adjustment

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○ Smooth the data with a central moving average of s points (s is the number

of seasons in the year)

○ Calculate - (seasonal difference for each period)

○ Find the average seasonal difference of each season (quarterly, monthly)

○ Calculate the Scaling Factor (i =)

○ Adjust to get (seasonally adjusted value)

● Step 3: Estimating the trend function T and forecasting

● Step 4: Incorporating seasonal factors S to give the final forecast result

2.3.2 For multiplicative model

The components of the time series depend on each other →

- : Irregular component

● Step 1: Data identification (multiplicative model)

● Step 2: Separating the seasonal factor - seasonality adjustment

○ Smooth the data with a central moving average of s points (s is the number

of seasons in the year)

○ Calculate (seasonal ratio for each period)

○ Find the average of the seasonality ratio of each season (quarterly,monthly)

○ Calculate the Scaling Factor (i =)

○ Adjust to get (seasonally adjusted value)

● Step 3: Estimating the trend function T and forecasting

● Step 4: Incorporating seasonal factors S to give the final forecast result

time series data to either better understand the data set or to predict future trends Thismodel is a form of regression analysis that gauges the strength of one dependent variablerelative to other changing variables ARIMA model is applied in cases where the timeseries data is non-stationary and needs differencing steps in order to be appropriatelyestimated

An ARIMA model consists of 3 parts, as denoted in its acronym The “AR” - AutoRegressive - part of ARIMA refers to a model that shows a changing variable thatregresses on its own lagged or prior values The “MA” - Moving Average - part indicatesthat the regression error is actually a linear combination of error terms whose valuesoccurred simultaneously and at various times in the past The “I” (for "Integrated")represents the differencing of raw observations in which the data values have beenreplaced with the difference between their values and the previous values to allow for thetime series to become stationary The purpose of each of these features is to make themodel fit the data as well as possible The process of fitting an ARIMA model issometimes referred to as the Box-Jenkins method ARIMA stands for Auto-RegressiveIntegrated Moving Average

AR (Auto Regression): A model that uses the dependent relationship between an

observation and some number of lagged observations p is a parameter of how manylagged observations are to be taken in

I (Integrated): A model that uses the differencing of raw observations (e.g.

subtracting an observation from the previous time step) Differencing in statistics is atransformation applied to time-series data in order to make it stationary This allows theproperties to not depend on the time of observation, eliminating trend and seasonality andstabilizing the mean of the time series

MA (Moving Average): A model that uses the dependency between an

observation and a residual error from a moving average model applied to lagged

observations q is a parameter of how many lagged observations are to be taken in.Contrary to the AR model, the finite MA model is always stationary.

ARIMA models provide another approach to time series forecasting Exponentialsmoothing and ARIMA models are the two most widely used approaches to time seriesforecasting and provide complementary approaches to the problem While exponentialsmoothing models are based on a description of the trend and seasonality in the data,ARIMA models aim to describe the autocorrelation in the data

ARIMA models may or may not involve the calculations of seasonal factors,depending on the data Non-seasonal ARIMA models are generally denotedARIMA(p,d,q) where parameters p, d, and q are non-negative integers, p is the order(number of time lags) of the autoregressive model, d is the degree of differencing (thenumber of times the data have had past values subtracted), and q is the order of themoving-average model Seasonal ARIMA models are usually denotedARIMA(p,d,q)×(P,D,Q)s, where s refers to the number of periods in each season, and theuppercase P,D,Q refer to the autoregressive, differencing, and moving average terms forthe seasonal part of the ARIMA model

2.4.2 Model

AR model: The term auto regression indicates that it is a regression of the variable

against itself Similar to the multiple regression model, where we forecast the variable ofinterest using a linear combination of predictors, in an autoregression model, we forecastthe variable of interest using a linear combination of past values of the variable Thus, anauto-regressive model of order p, or AR(p), can be written as:

In which:

- : white noise

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- : the constant level of the series

MA model: Rather than using past values of the forecast variable in a regression, a

Moving Average model uses past forecast errors in a regression-like model A MovingAverage order q, or MA(q), is written as follows:

In which:

- : the level (mean) of the process

- : white noise

- : depends on previous values of the errors

ARMA model: An ARMA, short for auto regressive-moving-average, model

involves both the aforementioned AR and MA models By combining the processes, anARMA(p,q) model is written as:

Orders p and q in an ARMA model are determined from the patterns of the sampleautocorrelations and partial autocorrelations

ARIMA model: By the same token, the full model of an integrated ARMA

(ARIMA) with difference steps, for example of ARIMA(p,1,q) is:

For ARIMA(p,d,q)×(P,D,Q)s, we have:

- p = number of non-seasonal autoregressive (AR) terms

- d = number of non-seasonal differences

- q = number of seasonal moving average (MA) terms

- P = number of seasonal autoregressive (SAR) terms

- D = number of seasonal differences

- Q = number of seasonal moving average (SMA) terms

2.4.3 Process

● Step 1: Check for stationarity of the series If the series is not stationary, transform

it into a stationary series

● Step 2: Determine p, q using ACF and PACF plots.

● Step 3: Estimate the model

● Step 4: Check for model’s adequacy:

○ Random residual

○ Is the term of the highest lag order significant? If not, reduce the lag orders(p, q)

○ Quality of the forecast (MAPE <=5%)

● Step 5: Forecasting with the model

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SECTION 3: FORECASTING RESULTS

3.1 Nạve model adjusted for trend and seasonality method

In order to forecast the future revenue of PepsiCo, we change the range from2010Q1 - 2023Q2 to 2012Q1 - 2024Q4 Through estimation by Naive model adjusted fortrend and seasonality, we get the following results:

t +1 = Y t +1-4 + (Y t +1-4 – Y t + 1-8)

• : the forecast made at time t for time (t + 1)t+1

• Yt+1-4: the actual value at time (t + 1) of the previous year

• Yt+1-8: the actual value at time (t + 1) of 2 years ago

Command:

genr yf1 = y(-1)

genr yf2 = y(-1) + y(-1) - y(-2)

genr yf(3) = yf(-4)

genr yf4 = y(-4) + y(-4) - y(-8)

genr rmse4 = @sqrt(@mean((y - yf4)^2))

genr mape4 = @mean(@abs((y - yf4)/y))