David J Romano Associates

ARIMA Forecasting and Monte Carlo Simulation

Main Content

Managing Risk & Uncertainty


Across the full spectrum of business, managing Risk and Uncertainty is key to success.

Financial Planning & Forecasting

Business Planning & Forecasting

Investment Modeling

Optimized Pricing Models

Inventory Management

Sales Planning

Manufacturing Process Optimization

Product Mix Optimization

Project Management Cost / Time Estimation

Minimizing Risk & Uncertainty

Whatever decision you need to make, your decision will be made most robust by the creative use of advanced analytical and statistical tools to minimize Risk and Uncertainty.

There are two key approaches to minimizing Risk & Uncertainty:

Forecasting – Using past data to make the best possible estimate of a future outcome. ARIMA based techniques are excellent for this.

Simulation – Using what you already know about the way elements of a problem interact to make a probability based estimation of future outcomes. Monte Carlo Simulation is excellent for this.

The best approach is always the one that is most appropriate to the type of Risk and Uncertainty you need to control.

We’re always happy to have an initial, no obligation, discussion to establish the best way forward.

Just give us a call on
+44 (0)7948 308 868

A 260 Day Forecast of GBP v EUR

This is an example 260 day ARIMA forecast along with Monte Carlo Simulation of the GBP v EUR forecast.

Data from 04/01/2000 to 07/07/2019 showing 1,000 historic data points with a 260 data point forecast.

NOTES

  1. Forecast is based on the last 5062 days, of which only the last 1000 are showing on the graph.
  2. Left hand scale is the value of EUR brought by 1 GBP
  3. Bottom scale is in currency market trading days, counted from the start of the data series.
  4. Actual history data is shown to the left of the vertical line.
  5. The ARIMA forecast values are shown by the red line to the right of the vertical line.
  6. Each of the thin blue lines to the right of the vertical line represent an individual Monte Carlo Simulation. There3 are 100 individual simulations in this model run.
  7. The orange area in the curve to the right above/below the mean forecast line defines the range on each of the forecast days where the prediction probability is between 5% and 95%, thus the extreme forecasts are excluded.
  8. The 5% / 95% boundary gets wider the further in time from the last data point due to the buildup of uncertainty.
  9. The density of simulation forecast line overlap gives the best indication of short term movements.


You should not rely on this example forecast.

Click image to see the Full Size Forecast in new tab

How We Do It So Cost-Effectively

Simply put, we use Incremental Prototyping.

For most problems the 80/20 rule is remarkably useful.

By using minimal time and resources we can usually get a clear picture of how how much uncertainty could be removed and what the incremental cost of removing additional uncertainty would be.

Foe most real world problems getting an 80% improvement at minimal cost is often good enough.

To paraphrase an idea conventionally ascribed to Pliny the Elder “If you can frighten an elephant with a mouse, why buy anything bigger than a mouse ?” It may not be a true saying, but it neatly sums up our approach to cost effectiveness.

We believe that the best model is the simplest model needed to make a difference and that further elaboration of a model beyond this point  just reduces cost-effectiveness.

ARIMA Forecasting Methods

ARIMA – Auto-Regressive Integrated Moving Average

These models are fitted to time series data to better understand the data and to predict future outcomes (values) in a the time series.

Examples of use would be to predict:

Call center loading

Seasonal sales demand

Short-term exchange rate movements

For those with a technical interest in the ARIMA technique go to the following links:

MIT ARIMA Time Series Forecasting Video Course Module

ARIMA Theoretical Definition

Monte Carlo Simulation Methods

Monte Carlo Methods – a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results.

These models are fitted to cross-impacting multi-dimensional data to better understand the data and to predict future outcomes (states).

Examples of use would be to predict:

Optimum Pricing to Maximize Revenue

Project Management Cost Estimation vs Budget

Portfolio Optimization

For those with a technical interest in the Monte Carlo Simulation technique go to the following links:

MIT Monte Carlo Simulation Video Course Module

Monte Carlo Simulation Theoretical Definition

David J Romano Associates

On LinkedIn

Consulting Services

We can provide you with the advice you need to manage Risk and Uncertainty.

Outsourcing Services

We can Build, Run and Report the Results from the Risk and Uncertainty models necessary to support your management information needs on a one-off or regular basis.

Training Services

We can provide the training required to enable you to understand and benefit from the use of the best techniques for Risk and Uncertainty management.

Registered Office

227A West Street, Fareham, Hampshire, PO16 0HZ, UK.

+44 (0)7948 308 868

Contact Us

Client Offices

London – Glasgow – Portsmouth – Milan – Paris