Why predict returns instead of prices in financial time series?

Price levels are usually non-stationary: their mean and variance change over time. Returns, especially log returns, are typically closer to stationary, so their statistical relationships are more stable and less likely to produce spurious regression or forecast results.

Are financial time series returns more stationary than prices?

Usually, yes. Differencing prices into simple or log returns removes much of the trend in the price level. Returns still need to be tested because volatility can change over time and extreme observations can affect the result.

What is a time series in finance?

A time series is a sequence of observations indexed over time, such as daily stock prices or returns used to study trends, seasonality, and volatility.

Why does stationarity matter?

Stationary data has stable statistical properties over time, which makes many forecasting and modeling techniques more reliable and interpretable.

What are moving averages used for?

Moving averages smooth short-term noise and can help reveal underlying trend direction in price or return data.

Quantitative Methods

Financial Time Series Analysis: Why Model Returns Instead of Prices?

Financial time series analysis explains how prices, returns, volatility, and other financial data evolve through time. The key modeling choice is often simple: use returns instead of raw prices when stationarity matters.

5 core techniques explainedReturns vs. prices clarifiedApplied to stock market data

Daily Statistics Statistics Guide Time Series Guide Forecasts Guide Other Data & Research

Financial time series analysis studies how data changes over the course of time. Understanding the mathematical structure of that data — and how it applies to time series pricing — is the foundation of this field of study. All price data of a stock, change in Net Income Year-over-Year, interest rate fluctuations, and so much more is plotted with a time series. Model development including trend analysis, volatility, and forecasting rely on the foundation of financial time series analysis.

This guide introduces the core concepts of time series analysis and explains how techniques that are often applied to financial markets.

Why Predict Returns Instead of Prices?

In finance, raw stock prices are usually non-stationary: they can drift, and their mean and variance can change over time. Simple returns and log returns are generally more stationary because they measure the change from one observation to the next. That makes returns a more reliable input for regression, autocorrelation analysis, and many forecasting models. This does not mean returns are perfectly predictable. It means the model is working with a more stable statistical series and can test its assumptions more honestly.

What is a Time Series?

A time series is a sequence of data points collected at successive points in time — usually at uniform intervals. In financial markets, time series are everywhere: daily closing prices, quarterly earnings values, intraday bid-ask spreads, and rolling volatility estimates are all examples. The defining characteristic is that order matters. Time goes from point 1 to 2 to 3... and values must match that. It can't jump from point-in-time 1 to 3 then back to 2, etc. Unlike a cross-sectional dataset (e.g. each availble stock's current price at a given time), each value in a time series is tied to a specific moment, and there is only one Y value for each given X value for time. We use a time series to measure changes over time for one option, and we use a cross-sectional analysis to measure changes between options given an instant in time. Time series analysis tries to find meaning in why the datapoints change over time.

Historically, stock prices have been seen to behave with a sort of Brownian Motion (ie. randomness) so a time-series analysis of stock prices, and "trying to predict future prices" can be seen as futile. We agree. However, Systems Capital would like to provide some insight into this discussion. One certainty we find in investing is that if we invest for the long term with good people doing good work, our investment appreciates. We find it incredibly valuable (and perhaps even mandatory) that we track our managers' performance over time, and play our role as owners as best as we can. Performing a time-series analysis on Net Income Year-Over-Year, the company's historic solvency ratios or credit scores, or even the performance of the management's publicly stated goals over time helps to see how they have changed over time. This is something we do for all our investments, and we find this application of time-series analysis to be largely beneficial for our investment portfolio. In addition, this sort of analysis does allow us to better predict future prices - albeit more long-term in practice. By defining characteristics that are reasonable within the comanies historic performance, we can set future estimated price targets (e.g. if all else stays the same, but we can expect the company to lower their cost of revenue by 50% by the end of the year, we can have a better estimate of what the stock price will be by the end of the year.)

This article will go over some major concepts that firms consider when modelling a time series.

Stationarity: Why Returns Are Used Instead of Prices

Before applying most forecasting or modeling techniques, a time series must satisfy a property known as stationarity. A stationary series has a constant mean, constant variance, and an autocorrelation structure that does not change over time. Intuitively, a stationary series oscillates around a fixed level rather than trending steadily upward or downward.

Raw stock price levels are almost never stationary — prices drift over time, causing their mean and variance to change continuously. Daily log returns, however, are typically much closer to stationary. Transforming a price level into a return series by taking first differences is therefore a standard pre-processing step before building any model. The Augmented Dickey-Fuller (ADF) test is the most widely used statistical tool for confirming stationarity. Failing to ensure stationarity before modeling often leads to spurious results — apparent relationships that dissolve when examined properly. Working in return space rather than price space is one of the most important habits in quantitative finance.

Autocorrelation

Autocorrelation measures the degree to which a time series is correlated with its own past values. High autocorrelation at lag 1 means that if yesterday's return was positive, today's is more likely to be positive as well. Near-zero autocorrelation suggests returns are essentially random from one period to the next, consistent with the behavior expected in a highly efficient market.

The Autocorrelation Function (ACF) plot visualizes this by computing the correlation between the series and lagged copies of itself at each lag. By definition, lag 0 always produces a correlation of 1.0 — a series is perfectly correlated with itself. If the ACF decays gradually, the series has persistent momentum. If it drops immediately to near zero, consecutive returns are largely independent. In practice, daily equity returns often show near-zero autocorrelation in raw returns, but meaningful autocorrelation in squared returns, where today's large move predicts a large move tomorrow, even if the direction is unknown is found in volatility modeling frameworks like GARCH (Generalized Autoregressive Conditional Heteroskedasticity).

Moving Averages

Moving averages are among the most popular applied time series tools in finance. They are largely used in day-trading. A Simple Moving Average (SMA) smooths a noisy series by computing the arithmetic mean of a rolling window of n observations. An Exponential Moving Average (EMA) assigns decreasing weights to older observations, making it more responsive to recent price changes without entirely discarding historical context.

How different windows of moving averages intersect with others (like the MA for a 20 Day window and a 50 Day window) are a popular signal. When a short-period MA crosses above a long-period MA, it may indicate the beginning of an upward trend. The reverse signals a potential downtrend. The appeal of moving averages is their simplicity — they require no assumptions about the distribution of returns, they adapt naturally to different time frequencies, and they can be combined in straightforward ways. Their main limitation is that they are inherently lagging indicators, responding to price changes only after they occur. This lag can reduce performance in choppy markets. Moving averages are most often applied to price charts to derive patterns within intraday performance.

ARIMA Forecasting

ARIMA — AutoRegressive Integrated Moving Average — is a classical statistical model for forecasting time series. It combines three components: the autoregressive (AR) term uses past values of the series to predict future values; the integrated (I) term differences the series to achieve stationarity; and the moving average (MA) term uses past forecast errors to refine predictions. The three parameters are written as ARIMA(p, d, q), where p controls the AR order, d the degree of differencing, and q the MA order.

In quantitative finance, ARIMA and its extensions are used to generate short-term price forecasts, model volatility dynamics, and identify deviations from expected behavior. The confidence intervals produced by an ARIMA model widen as the forecast horizon extends — a natural reflection of uncertainty growing over time. Some use these time intervals not only for point estimates but to set probabilistic bounds around expected outcomes and structure risk accordingly. ARIMA models have some extensions as well. SARIMA accommodates seasonal patterns, and GARCH models — which can be viewed as time series models for conditional variance — directly addresses the volatility clustering commonly observed in equity returns.

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How to Use These Together

Time series analysis is most powerful when its tools are layered together. Begin by testing for stationarity before building any model — working on the raw price level rather than returns is one of the most common and costly mistakes in quantitative finance. Use the ACF plot to identify whether autocorrelation exists at meaningful lags, and decide whether a momentum-based or mean-reversion framework is more appropriate for the security in question. Apply moving averages as a real-time trend filter to smooth out daily noise before acting on signals. Deploy ARIMA or its extensions when structured short-term forecasts with explicit confidence bounds are needed. Or don't do any of this, and just have a better understanding of time series modelling.

Knowing all of this allows these frameworks to provide a more complete picture of how a security behaves through time, and it allows you to find the answers to your questions, even if the question is "How should I expect the company to perform this year?". For a practical application of these ideas, see our market forecasting and forecast analysis guide, which builds directly on the stationarity concepts above.