RatioPlotter.eu - Seasonality Plotter

Plot Seasonality for Ticker

Enter one financial asset ticker (e.g. T-USO-SplitAdjClose). You can copy tickers into a basket using the ticker selector.

Suggested Seasonality Plots (All allowed for non-subscribers)

Plot Icon Legend: (No medal icon) Free Plot: Free and unlimited. Does not require login. Premium Plot: Allowed for non-subscribers up to 8/month. Requires Google Login. Includes all tickers not in the list below.

Understanding Seasonality Models:

Find the best seasonality models ranked in: Seasonality insights page.

Read an article explaning how to interpret a seasonality model using the legend below: MSCI World Seasonality, Sep 2026.

Seasonality Chart Legend:

Colored lines (Normalized YTD for various years):

One line is shown for each historical year; the year lines are coloured in the sequence of the rainbow hues. This implements Normalized YTD logic by finding the first valid price of the year (usually Jan 1st) and recalculating the rest of that year as a percentage deviation from that start price.

Thick gray line (Composite, the seasonality curve = median of colored lines):

This is a robust aggregation of the coloured lines using the median rather than the mean. Why median? If one year had a massive 50% crash in March, the Median line will ignore it, whereas an Average line would drag the whole seasonal chart down, giving you a false bearish signal.

Black dotted line: the current year to date

This represents the current year. It is vital for seeing where the current price is trading relative to historical trends.

The Bottom Panel: flattened grey and black dotted lines.

We flatten the median seasonal trend to remove its exponential growth/decay component from start to end point. The method to flatten the current year is not by removing start to end exponential growth/decay, but by doing a log linear regression and removing the mean growth, this is more robust for the case where the start and the end point values are just one observation and not the median.

Capital Deployer's Guide to the Seasonality Engine:

We suggest using the seasonality as a complement to another model such as Engle-Granger. When the two models point in the same direction we typically have a better opportunity for an entry.

This seasonality chart doesn't just show historical averages; it rigorously backtests the calendar shape to prove whether the seasonal signal actually possesses predictive edge for deploying capital.

The layout is broken down into interconnected layers:

(A) The master smoothed median, utilizing all available historical data to give you as much forward predicting power as possible.

(B) A strictly isolated prediction curve based on the training data (i.e. all data minus the last 380 days).

The Out-of-Sample Holdout Engine:

To prevent "look-ahead bias" (the illusion of predictability caused by testing a model on the same data used to build it), the engine physically clamps the timeline. It hides the last 380 days (Curve C) from the math engine entirely, forcing the system to predict the future using only older data (Curve B). It runs this holdout test 3 consecutive times to ensure a single lucky year doesn't inflate the asset's predictive score.

The 3 "Hit Rate" Metrics (R-Squared):

1. Standard R² of B vs C: Measures raw directional accuracy. While useful, this can be a trap. If an asset is in a massive multi-year secular bull market, it goes up regardless of the calendar month or year, creating a falsely high Standard R². This is not the pure yearly seasonality, it contains the secular growth or decay.

2. Detrended R² (curves not shown): To defeat the secular growth trap, this metric mathematically strips out the historical compound growth rate found in the seasonal trend from both the prediction and the reality before scoring them for correlation. But what if the historical compound growth is reflecting a bull market positive growth rate, but the reality of the hold out data is that we entered a bear market? The thir R² measurement below address this case. You should know when the last 380 days changed secular trend and use the third R² and not the second.

3. Pure Seasonal R² of B' vs C': The ultimate shape-correlation test. It completely neutralizes macroeconomic noise by using Ordinary Least Squares (OLS) regression to flatten both the prediction (B') and the actual holdout (C') to a zero-slope horizontal axis. To avoid the "U-shaped residual" loophole common in exponentially compounding assets, the engine applies log-linear regression to properly extract the pure seasonal shape (what we call flattened).

Trading Notes & Guide

Ticker Data Usage, Data Sourcing and Ticker Functions

Ticker Data Sources

Our data is provided from a variety of sources: The Federal Reserve (FED-* tickers), The World Bank (WB-* tickers), The International Monetary Fund (IMF-* tickers), Tiingo (T-* tickers covering: stocks, ETFs, etc), Eurostat (ES-* tickers), Ourselves (MATH-* tickers), Yourself (USR-* tickers for uploaded). The ticker data sources vary according to ticker prefix as you can see. Our ticker selector allows browsing each ticker and their description and placing them on a basket for use. The menu has links allwoing the upload of your own data which goes into the USR-* ticker space.

Default Ticker Column Projections & Adjustments

Let's take T-GOOGL as an example. When the projection variable is left blank, the ratio plotter will use the default projection variable which is -AdjClose (close price adjusted for both dividends and splits). This means that when you input T-GOOGL into the ratio plotter it will actually plot the "Tiingo split and dividend adjusted close price" of GOOGL: T-GOOGL-AdjClose (T-GOOGL-AdjClose by T-MSFT-AdjClose). If you want to plot the split (but not dividend) adjusted close price of GOOGL you can input T-GOOGL-SplitAdjClose. All projection columns are provided by Tiingo, with exception of the -SplitAdjClose column which is calculated by our system. For a complete explanation for beginners see our article: Understanding column projections.

ADD() Element-wise adding

The ADD() function performs element-wise addition between two vectors, or between a vector and a literal scalar value. Example: ADD(T-AAPL, T-MSFT) or ADD(T-GLD, 10.5).

CLOSE_GAPS() Interpolating and extrapolating sparse data

The CLOSE_GAPS() function resolves interior and exterior `NaN` gaps in sparse datasets (like European Union Eurostat macroeconomic vectors). It requires 4 arguments: the ticker, interpolation method ('LINEAR'), extrapolation method ('FORWARD_FILL', 'NONE', 'LINEAR'), and extrapolation days. Example: CLOSE_GAPS(ES-teicp000-coicop18, 'LINEAR', 'FORWARD_FILL', 60).

CURVE_FROM_VECTOR() Custom data vectors

The CURVE_FROM_VECTOR() function allows transforming your own data vectors into plottable data. It creates a vector from user-entered data points, useful for proprietary data. Example usage: CURVE_FROM_VECTOR([198.27, 211.92, 245.12, 281.72, 318.27], '2026-06-30', 'last', '1y', 'linear', 'forward_fill'). Arguments represent the array of values, anchor date, anchor position ('first' or 'last'), frequency ('1y', '1q', '1m'), interpolation ('linear', 'forward_fill'), and extrapolation ('none', 'forward_fill', 'linear').

LAG() Time-shifted underlying vector

The LAG() ticker function is used to create a lagged version of an asset. This shifts a dataset to the right by an amount of days equal to the lag value. To write custom LAG() tickers, simply input your ticker of choice and lag value between the parenthesis, separated by a comma. Example: LAG(T-AAPL, 10). It is highly useful for autocorrelation studies.

LINEAR_COMBINATION() Weighted sum of multiple vectors

The LINEAR_COMBINATION() function calculates a weighted mathematical sum across multiple vectors. It takes two arrays as arguments: an array of coefficients and an array of tickers or expressions. Example: LINEAR_COMBINATION([1.5, -0.5], [T-AAPL, T-MSFT]).

LOG() Logarithmic transformation

The LOG() function applies a logarithmic transformation to a vector given a specific mathematical base. It accepts the ticker and the mathematical base as arguments. Example: LOG(T-GOOGL, 2) or LOG(T-MSFT, 10). If you want you can use EPSILON constant which is not a natural logarithm constant, but just a logarithm on a tiny base: LOG(T-SPY, EPSILON). We encourage using LOG on the base two as it is the fastest to compute for you and will allow caching of the computation for others to benefit. The LOG on base 2 will also mean you are measuring how long it takes for the time series to double, a difference in 1 point is a doubling.

LOOK_FORWARD() Shifting data forward in time

The LOOK_FORWARD() function is the mathematical inverse of LAG(). It brings future values forward in time to the current date coordinate, shifting the vector left toward the epoch. Example: LOOK_FORWARD(T-AAPL, 30). The second argument 30 is the number of days to look forward. All our data for time series is measured in days.

MATH- Custom Mathematical Tickers

The MATH- tickers are custom, idealized mathematical baseline tickers generated by our system (e.g. MATH-CAGR_PCT-2 for 2% exponential growth, MATH-CONST_VEC-1 for a constant flatline value of 1). To find the list of valid MATH tickers go to the Ticker Selector Page. Note that MATH tickers have a truth boundary projected far into the future (9999-12-31).

MINUS() Element-wise subtraction

The MINUS() function calculates the element-wise subtraction of the second argument from the first. It supports vector-vector, vector-scalar, and scalar-vector subtraction. Example: MINUS(T-AAPL, T-MSFT).

MOVING_AVERAGE() Trailing Simple Moving Average

The MOVING_AVERAGE() function computes a simple rolling mean over a specified lookback window of days. Example: MOVING_AVERAGE(T-SPY, 200) calculates the 200-day trailing moving average.

MULT() Element-wise multiplication

The MULT() function computes the element-wise multiplication of two synchronized vectors. Example: MULT(T-COM, T-USDCHF) performs a currency conversion of the T-COM broad commodity investment basket to Swiss Francs (most of our tickers are in USD and that ticker price currency can be seen on the ticker selector page). T-COM is the: DIREXION AUSPICE BROAD COMMODITY STRATEGY ETF.

RAT() Calculating Ratio Between Two Tickers

The RAT() ticker function works by calculating the relative outperformance (division) between two tickers as a new dataset. To write custom RAT() tickers, simply input your two tickers of choice separated by a comma. Example: RAT(T-AAPL, T-MSFT). Example of comparing Google's outperformance to an idealized CAGR curve: RAT(T-GOOGL,T-MSFT)/MATH-CAGR_PCT-2 (requires login with Google).

REGRESSION() and RESIDUALS() Functions

(1) The REGRESSION or RESIDUAL functions are reserved for paying users, apart from the free tier REGRESSION examples present on the log plot page.

(2) When the REGRESSION() function is the outermost function of the expression and is used on the log plotter, it will cause a nice regression plot canvas to display the fitting line and useful regression statistics such as ADF probability and R².

If used on the regular ratio plotter page, it will plot the residuals vector. Example: REGRESSION(LOG(T-URTH,2)) (this example requires subscription as it uses the LOG function).

The REGRESSION function is very good at modelling time series that grow following a linear trend. Most financial assets grow following an exponential trend, which means that if we apply the LOG function to this asset ticker we obtain a linear trend which can be modelled by the REGRESSION function. Try it, try plotting just LOG(T-GOOGL) to see this straight line tendency.

RET() Rolling Percentage Return

The RET() function calculates the trailing rolling percentage return of an asset over a specified day window. Example: RET(T-SPY, 30) measures the rolling 30-day percentage performance. The return for a day is always measured looking back at the last x days (30 in the example), otherwise we would introduce look-ahead bias into our models of returns. To calculate forward returns you can combine the two functions RET(LOOK_FORWARD(T-GOOGL,30),30). Easy right?

ROLLING_SLOPE() Calculating slope, velocity, or derivating

Calculates the rolling derivative/velocity of an underlying vector. Example: ROLLING_SLOPE(IMF-NGDPD-CHN, 400, 1). The second argument (400) is the lookback window in days to calculate the smoothed slope. The third argument (1) determines the scalar output granularity (e.g., 1 for daily velocity, 365 to annualize the velocity). Example: China GDP Velocity.

SIMUL_TICKER_DIV_REINVEST() Plotting Dividends Reinvested at Your Portfolio Return Rate

You can do this with the function: SIMUL_TICKER_DIV_REINVEST(T-MSFT,0.25,1,'2022-08-01'). This is a function available only for users with the advanced subscription. The first argument is the Ticker simulated, the second is your portfolio CAGR rate (in this case 0.25 = 25% yoy, applied dynamically daily). The third argument is the initial investment in the currency of the stock ticker. The last argument is the start date. See our article on dividend reinvestment simulation.

VOLATILITY() Annualized Rolling Volatility

The VOLATILITY() function calculates the annualized rolling standard deviation of 1-day returns over a designated window of time. Example: VOLATILITY(T-SPY, 50) measures the annualized volatility of the S&P 500 utilizing a 50-day rolling lookback window. The Scatter plot tool has some examples of the VOLATILITY function.

Z_SCALE() Z scaling, bringing data to the normal curve Z score scale, normalizing

You can do this with the function: Z_SCALE(). Examples: Z_SCALE(T-MSFT), Z_SCALE(RAT(T-GLD,T-SLV)), Z_SCALE(ROLLING_SLOPE(T-COM,90,1)). This brings absolute price vectors or ratios to a standardized Normal Curve (Mean 0, StdDev 1) for macro-economic cycle alignment. This function is available only for users with the advanced subscription. The Buffett Indicators Tool allows plotting the Z-Scale spread of the country ETF price to its GDP figures.