Financial institutions and corporations as well as individual investors and researchers often use financial time series data (such as asset prices, exchange rates, GDP, inflation and other macroeconomic indicators) in economic forecasts, stock market analysis or studies of the data itself.

But refining data is key to being able to apply it to your stock analysis. In this article, we'll show you how to isolate the data points that are relevant to your stock reports.

Cooking Raw Data
Data points are often non-stationary or have means, variances and covariances that change over time. Non-stationary behaviors can be trends, cycles, random walks or combinations of the three.

Non-stationary data, as a rule, are unpredictable and cannot be modeled or forecasted. The results obtained by using non-stationary time series may be spurious in that they may indicate a relationship between two variables where one does not exist. In order to receive consistent, reliable results, the non-stationary data needs to be transformed into stationary data. In contrast to the non-stationary process that has a variable variance and a mean that does not remain near, or returns to a long-run mean over time, the stationary process reverts around a constant long-term mean and has a constant variance independent of time.

Copryright © 2007
Figure 1

Types of Non-Stationary Processes
Before we get to the point of transformation for the non-stationary financial time series data, we should distinguish between the different types of the non-stationary processes. This will provide us with a better understanding of the processes and allow us to apply the correct transformation. Examples of non-stationary processes are random walk with or without a drift (a slow steady change) and deterministic trends (trends that are constant, positive or negative, independent of time for the whole life of the series).

Copryright © 2007
Figure 2
  • Pure Random Walk (Yt = Yt-1 + εt )
    Random walk predicts that the value at time "t" will be equal to the last period value plus a stochastic (non-systematic) component that is a white noise, which means εt is independent and identically distributed with mean "0" and variance "σ²". Random walk can also be named a process integrated of some order, a process with a unit root or a process with a stochastic trend. It is a non mean reverting process that can move away from the mean either in a positive or negative direction. Another characteristic of a random walk is that the variance evolves over time and goes to infinity as time goes to infinity; therefore, a random walk cannot be predicted.
  • Random Walk with Drift (Yt = α + Yt-1 + εt )
    If the random walk model predicts that the value at time "t" will equal the last period's value plus a constant, or drift (α), and a white noise term (εt), then the process is random walk with a drift. It also does not revert to a long-run mean and has variance dependent on time.
  • Deterministic Trend (Yt = α + βt + εt )
    Often a random walk with a drift is confused for a deterministic trend. Both include a drift and a white noise component, but the value at time "t" in the case of a random walk is regressed on the last period's value (Yt-1), while in the case of a deterministic trend it is regressed on a time trend (βt). A non-stationary process with a deterministic trend has a mean that grows around a fixed trend, which is constant and independent of time.
  • Random Walk with Drift and Deterministic Trend (Yt = α + Yt-1 + βt + εt )
    Another example is a non-stationary process that combines a random walk with a drift component (α) and a deterministic trend (βt).It specifies the value at time "t" by the last period's value, a drift, a trend and a stochastic component. (To learn more about random walks and trends, see our Financial Concepts tutorial.)

Trend and Difference Stationary
A random walk with or without a drift can be transformed to a stationary process by differencing (subtracting Yt-1 from Yt, taking the difference Yt - Yt-1) correspondingly to Yt - Yt-1 = εt or Yt - Yt-1 = α + εt and then the process becomes difference-stationary. The disadvantage of differencing is that the process loses one observation each time the difference is taken.

Copryright © 2007
Figure 3

A non-stationary process with a deterministic trend becomes stationary after removing the trend, or detrending. For example, Yt = α + βt + εt is transformed into a stationary process by subtracting the trend βt: Yt - βt = α + εt, as shown in Figure 4 below. No observation is lost when detrending is used to transform a non-stationary process to a stationary one.

Copryright © 2007
Figure 4

In the case of a random walk with a drift and deterministic trend, detrending can remove the deterministic trend and the drift, but the variance will continue to go to infinity. As a result, differencing must also be applied to remove the stochastic trend.

Using non-stationary time series data in financial models produces unreliable and spurious results and leads to poor understanding and forecasting. The solution to the problem is to transform the time series data so that it becomes stationary. If the non-stationary process is a random walk with or without a drift, it is transformed to stationary process by differencing. On the other hand, if the time series data analyzed exhibits a deterministic trend, the spurious results can be avoided by detrending. Sometimes the non-stationary series may combine a stochastic and deterministic trend at the same time and to avoid obtaining misleading results both differencing and detrending should be applied, as differencing will remove the trend in the variance and detrending will remove the deterministic trend.

Related Articles
  1. Investing Basics

    What Does In Specie Mean?

    In specie describes the distribution of an asset in its physical form instead of cash.
  2. Economics

    Calculating Cross Elasticity of Demand

    Cross elasticity of demand measures the quantity demanded of one good in response to a change in price of another.
  3. Fundamental Analysis

    Emerging Markets: Analyzing Colombia's GDP

    With a backdrop of armed rebels and drug cartels, the journey for the Colombian economy has been anything but easy.
  4. Investing

    What is Descriptive Statistics?

    Descriptive statistics is the term applied to meaningful data analysis.
  5. Fundamental Analysis

    Create a Monte Carlo Simulation Using Excel

    How to apply the Monte Carlo Simulation principles to a game of dice using Microsoft Excel.
  6. Fundamental Analysis

    Emerging Markets: Analyzing Chile's GDP

    Chile has become one of the great economic success stories of Latin America.
  7. Mutual Funds & ETFs

    Top 4 Inverse Equities ETFs

    Explore analysis of some of the most popular inverse and leveraged-inverse ETFs that track equity indexes, and learn about the suitability of these ETFs.
  8. Investing

    Watch Your Duration When Rates Rise

    While recent market volatility is leading investors to look for the nearest exit, here are some suggestions for bond exposure in attractive sectors.
  9. Economics

    Explaining Capital Flows

    The movement of money for investing, trade or business production, is commonly referred to as capital flows.
  10. Forex Fundamentals

    How Foreign Exchange Affects Mergers and Acquisitions Deals

    Learn how foreign exchange rates can impact the flows of international merger and acquisition (M&A) transactions, and understand how deals can impact exchange rates.
  1. Is Colombia an emerging market economy?

    Colombia meets the criteria of an emerging market economy. The South American country has a much lower gross domestic product, ... Read Full Answer >>
  2. What assumptions are made when conducting a t-test?

    The common assumptions made when doing a t-test include those regarding the scale of measurement, random sampling, normality ... Read Full Answer >>
  3. What is the utility function and how is it calculated?

    In economics, utility function is an important concept that measures preferences over a set of goods and services. Utility ... Read Full Answer >>
  4. What are some of the more common types of regressions investors can use?

    The most common types of regression an investor can use are linear regressions and multiple linear regressions. Regressions ... Read Full Answer >>
  5. What types of assets lower portfolio variance?

    Assets that have a negative correlation with each other reduce portfolio variance. Variance is one measure of the volatility ... Read Full Answer >>
  6. When is it better to use systematic over simple random sampling?

    Under simple random sampling, a sample of items is chosen randomly from a population, and each item has an equal probability ... Read Full Answer >>

You May Also Like

Hot Definitions
  1. Gross Profit

    A company's total revenue (equivalent to total sales) minus the cost of goods sold. Gross profit is the profit a company ...
  2. Revenue

    The amount of money that a company actually receives during a specific period, including discounts and deductions for returned ...
  3. Normal Profit

    An economic condition occurring when the difference between a firm’s total revenue and total cost is equal to zero.
  4. Operating Cost

    Expenses associated with the maintenance and administration of a business on a day-to-day basis.
  5. Cost Of Funds

    The interest rate paid by financial institutions for the funds that they deploy in their business. The cost of funds is one ...
  6. Cost Accounting

    A type of accounting process that aims to capture a company's costs of production by assessing the input costs of each step ...
Trading Center
You are using adblocking software

Want access to all of Investopedia? Add us to your “whitelist”
so you'll never miss a feature!