Review For Exam III Chapters 8 And 9, Chapter 81 Auto Correc

Review For Exam Iii Chapter 8 And Chapter 9chapter 81autocorrelation

Review for Exam III--Chapter 8 and Chapter 9 Chapter . Autocorrelation · Consequence · Test for autocorrelation: Durbin Watson Test · Solution for autocorrelation 2. Regression with differences · Regression estimation · Checking on autocorrelation of residuals · Forecast 3. Regression with seasonal data using dummy variables Chapter . Components of ARIMA model: AR, I, and MA 2.

Fitting ARIMA model · Model identification · Time series plot · Autocorrelation graph · Partial autocorrelation graph · Model estimation · Model checking · Mean Squares (MS) · Ljung-Box Q statistics, Chi-squared test · Checking residuals · forecast 3. Fitting ARIMA model with seasonal data Ministry of Higher Education Colleges of Applied Sciences Business Administration Program Final Assessment - Semester Spring 2020 Following fill by the Lecturer: Course Code : BSMK2102 Course Title: Marketing Student’s ID Number: Student’s Name: Sending Date & Time: On 3rd May 2020 @ 12 noon Sending through: CAS Mail / Black Board ……. Submission Week: Week 16 / Week 17 Submission Date and Time: Starting from 8 am 9th May 2020 and ending at 11am 14th May 2020 Marks Scored: 20 Following fill by the Student: Date & Time of submission : On …May 2020 @ ….

Submitting through : CAS Mail/ Black Board ……….. Questions - Answer any FOUR (4 x 5 marks = 20 marks) 1. What do you mean by “Product Lineâ€? Discuss product line for Samsung Company. 2.

Assume any consumer product and discuss how the company segments its market and give a brief description/profile of the consumers of the product. 3. Pizza Hut was founded in June 1958 in Kansas, USA. Pizza Hut has been doing business in Oman since long time when they opened their first store in Muscat. Today many Pizza Hut stores sell pizza and other items across Oman.

Factors such as culture that operate in the domestic market also exist internationally. Discuss the key cultural factors Pizza Hut had to consider as it expanded into Oman 4. Large retail stores like Carrefour and Lulu provide many offers and take customer opinion on their product and services. Why do you think retail stores like Carrefour and Lulu relies so much on surveys to track customer opinions, preferences, and criticisms? What are the advantages of online questionnaires versus traditional surveys conducted over the phone or through the mail?

5. Discuss any three development/ changes in Marketing scenario in Oman. Explain with an example. Write your answer below: Business Administration Program Final Assessment Semester Spring 2020

Paper For Above instruction

Introduction

Understanding the concepts of autocorrelation, ARIMA models, and their application in time series forecasting is essential for advanced statistical analysis, particularly in economic, financial, and marketing data. The first part of this paper reviews key concepts from chapters 8 and 9, focusing on autocorrelation, the Durbin-Watson test, regression with differences, seasonal modeling, and ARIMA components. The second part discusses practical applications, including model identification, fitting, checking, and forecasting, emphasizing applications in retail, marketing, and international expansion scenarios.

Autocorrelation and Its Implications

Autocorrelation refers to the correlation of a time series with its own past values. It has significant implications in regression analysis because it violates the assumption of independence of residuals, potentially leading to inefficient estimates and misleading inferences (Box et al., 2015). The Durbin-Watson (DW) test is a common method used to detect autocorrelation at lag 1 in residuals of regression models. A DW statistic close to 2 suggests no autocorrelation, values approaching 0 indicate positive autocorrelation, and those near 4 suggest negative autocorrelation (Durbin & Watson, 1951).

When autocorrelation is present, solutions include transforming variables, using differenced data, or employing models explicitly designed to account for autocorrelation, such as ARIMA. Recognizing the consequence of autocorrelation is vital in ensuring valid regression inferences and accurate forecasting, especially in economic and marketing time series data, where autocorrelation is often observed due to underlying trends and seasonal patterns (Lütkepohl, 2005).

Regression with Differences and Seasonal Data

Regression with differencing involves transforming the dependent variable to achieve stationarity, which often helps mitigate autocorrelation issues. Estimating models on differenced data can improve model accuracy and validity (Chatfield, 2004). Checking the residuals' autocorrelation after model fitting, through plots and tests, ensures the appropriateness of the model.

Seasonal data require specialized modeling approaches. Dummy variables representing different seasons can be incorporated into regression models, allowing for seasonal effects analysis. Alternatively, models like Seasonal ARIMA (SARIMA) combine autoregressive and moving average components with differencing to capture both trend and seasonal patterns effectively (Box et al., 2015).

ARIMA Models: Components and Fitting Process

The ARIMA (AutoRegressive Integrated Moving Average) model combines three vital components: AR (AutoRegressive), I (Integrated), and MA (Moving Average). AR captures the relationship between an observation and a number of lagged observations; I involves differencing to attain stationarity; MA models the dependency between an observation and residual errors from a moving average process.

Model identification starts with exploratory data analysis, including plotting the time series, autocorrelation function (ACF), and partial autocorrelation function (PACF). These help determine the order of AR and MA terms. Model estimation applies maximum likelihood or least squares methods, followed by model diagnostics such as residual analysis, which checks for randomness and normality (Chatfield, 2004).

Tools like the Ljung-Box Q statistic and Chi-squared tests assess whether residual autocorrelations are statistically insignificant, confirming the model's adequacy. Once validated, the ARIMA model can be used for forecasting future data points, aiding decision-making processes in business contexts (Box et al., 2015).

Fitting ARIMA Models with Seasonal Data

When dealing with seasonal data, ARIMA models extend into SARIMA models, incorporating seasonal AR and MA terms, seasonal differencing, and seasonal dummy variables as needed. Identification involves examining seasonal patterns in the time series, using seasonal plots and seasonal ACF/PACF charts.

Fitting SARIMA models requires selecting the appropriate orders for seasonal and non-seasonal parts, fitting models through maximum likelihood, and validating through residual diagnostics. Forecasting with seasonal models enables precise predictions accounting for cyclical fluctuations—crucial for retail planning, inventory management, and marketing strategies (Box et al., 2015).

Practical Applications in Marketing and Business Expansion

Analyzing consumer behavior, segmentation, and cultural factors plays a significant role in business expansion, as illustrated by Pizza Hut’s entry into Oman. Understanding cultural sensitivities, preferences, and local customs is vital for success in international markets (De Mooij, 2010). For instance, adaptation of menus, marketing messages, and store layouts to align with local culture can significantly influence customer acceptance and brand loyalty.

Similarly, in retail environments like Carrefour and Lulu, surveys are critical tools for capturing insights into customer preferences, satisfaction, and criticisms. Online questionnaires offer advantages such as ease of distribution, rapid data collection, and analytical efficiency. They enable retailers to adapt quickly to changing preferences, optimize product offerings, and enhance customer experience (Bryman & Bell, 2015).

Furthermore, the evolving marketing landscape in Oman has seen shifts such as increased digital marketing adoption, rise in e-commerce activities, and enhanced international collaborations. These developments exemplify a dynamic environment where data-driven decision-making, aided by time series analysis models, plays a crucial role in strategic planning and competitive advantage.

Conclusion

In conclusion, the integration of time series techniques such as autocorrelation analysis, ARIMA modeling, and seasonal adjustments is essential for accurate forecasting and strategic business decisions. By understanding and applying these concepts, businesses can better anticipate trends, optimize marketing strategies, and effectively expand into international markets while accounting for cultural and consumer dynamics.

References

1. Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time Series Analysis: Forecasting and Control (5th ed.). Wiley.
2. Chatfield, C. (2004). The Analysis of Time Series: An Introduction. Chapman and Hall/CRC.
3. De Mooij, M. (2010). Global Marketing and Advertising: Understanding Cultural Paradoxes. SAGE Publications.
4. Lütkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer.
5. Durbin, J., & Watson, G. S. (1951). Testing for serial correlation in least squares regression: I. Biometrika, 38(1-2), 159-177.
6. Bryman, A., & Bell, E. (2015). Business Research Methods. Oxford University Press.
7. Hamilton, J. D. (1994). Time Series Analysis. Princeton University Press.
8. Gonzalez-Rodriguez, G., & de la Torre, L. (2020). Forecasting retail sales with seasonal ARIMA models. International Journal of Forecasting, 36(2), 529-542.
9. Makridakis, S., Wheelwright, S. C., & Hyndman, R. J. (1998). Forecasting: methods and applications. John Wiley & Sons.
10. Tsay, R. S. (2010). Analysis of Financial Time Series. Wiley.