Proposal Presentation

• Introduction and Background
• Literature Review
• Objective and Scope
• Methodology
• Plan and Schedule
• Expected Outcome

Cash Out

Over cash inventory

To optimize the amount of cash notes in the machine

• Automatic Teller Machine (ATM)
• ATM replenishment
• Dataset from NN5
• Time series
  • Exponential smoothing
  • ARMA
  • ARIMA

Luther Simjian

John Shepherd-Barron

• Cassettes are replaced by prepared full cassettes and are returned to a financial institution

• Time series is a collection of data recorded over a period of time—weekly, monthly, quarterly, or yearly.
• Time series forecasting is the use of a model to predict future values based on previously observed values.
• Examples: Dow Jones Industrial Average, Daily Temperature, Gold price

Patterns of Time Series

• Trend: long term movements in the mean
• Seasonality: cyclical fluctuations according to calendar
• Long-run cycle: cyclical fluctuations such as a business cycles
• Outliers: irregular patterns

To predict the value at the present time using the value at the previous time.

EQUATION AR(p)

\[ X_t = \Phi_1 X_{t-1} + \Phi_2 X_{t-2} + ... + \Phi_p X_{t-p} + \varepsilon_t \]

where \( \varepsilon_t \) is independent identically distributed (iid) with Normal Distribution of mean 0 and constant variance \( \sigma_\varepsilon^2 \)

“Past Error”

EQUATION MA(q)

\[ X_t = \varepsilon_t + \theta_1 \varepsilon_{t-1} + ... + \theta_q \varepsilon_{t-q} \]

where \( \varepsilon_t \) ~ \( N(0,\sigma_\varepsilon^2) \)

EQUATION ARMA(p,q)

\[ X_t = \Phi_1 X_{t-1} + ... + \Phi_p X_{t-p} + \varepsilon_t + \theta_1 \varepsilon_{t-1} + ... + \theta_q \varepsilon_{t-q} \]

For example ARMA(1,1)

\[ X_t = \Phi_1 X_{t-1} + \varepsilon_t + \theta_1\varepsilon_{t-1} \]

From ARMA(p,q)

\[ X_t = \Phi_1 X_{t-1} + ... + \Phi_p X_{t-p} + \varepsilon_t + \theta_1 \varepsilon_{t-1} + ... + \theta_q \varepsilon_{t-q} \]

\[ X_t - \Phi_1 X_{t-1} - ... - \Phi_p X_{t-p} = \varepsilon_t + \theta_1 \varepsilon_{t-1} + ... + \theta_q \varepsilon_{t-q} \]

• B is the backward operator

\[ (1-\Phi_1 B - ... - \Phi_p B^p) X_t = (1 + \theta_1 B + ... + \theta_q B^q)\varepsilon_t \]

\[ \Phi(B)X_t = \theta(B)\varepsilon_t \]

\[ ARIMA(p,d,q): \Phi(B)(1-B)^d X_t = \theta(B)\varepsilon_t \]

EQUATION Holt-Winters(\( \alpha \))

\[ F_{t+1} = \alpha X_t + (1-\alpha)F_t \]

where \( \alpha \) is a smoothing constant and \( 0 \leq \alpha \leq 1 \)

ARMA

• Can not handle seasonality or trend

ARIMA

• Not accurated long term forecast

Exponential smoothing

• Hard to find the best alpha (smoothing constant)
• Can not handle seasonality or trend

• Multi-intervention forecasting model for ATM, Ms. Wanicha Shithamarach, Ms. Apichaya Phannongwah, (2013).

• To create new forecasting model to optimize the amount of cash note inventory and apply the new model to data from NN5
• To compare with the existing model such as exponential smoothing, ARMA, ARIMA, and Multi-intervention model by using the mean absolute percentage error (MAPE) method.

• Use R language on Rstudio software to formulate the model and forecast data
• The data used in this project is from NN5
• Dataset is portioned into 2 parts
  • 80% in-sample
  • 20% out-sample
• This model will be created from using Exponential smoothing, ARMA, and ARIMA model
• Model is tested by the mean absolute percentage error (MAPE) \[ M = \frac{1}{n}\sum_{t=1}^{n} \left|\frac{A_t-F_t}{A_t}\right| \]

• Use the same distribution of data as the previous period

  EX. For week 9, use the distribution from week 1 and 5

  

• The accuracy of outcome from new forecasting model is expected to be better comparing with other existing models.
• The opportunity to publish this project