Markov Transition Matrix

• Bullish when the N-bar return is above the selected positive threshold
• Bearish when the N-bar return is below the selected negative threshold
• Neutral when the return stays between those thresholds

• After a bullish state, how often does the next state stay bullish?
• After a neutral state, how often does the next state turn bearish?
• Which current state has the strongest tendency to persist or reverse?

1. Choose an analysis timeframe.
2. Choose a lookback window in candles.
3. For each completed bar in that timeframe, the script computes the return from close[lookback] to the current close.
4. That return is classified as Bullish, Neutral, or Bearish using the threshold input.
5. Each one-step transition from the previous state to the new state is added to the cumulative matrix.

• The main value in each cell is the one-step transition probability for that row and column.
• The detail row under each cell shows P^2, P^3, and the raw transition count.
• The summary row shows the latest confirmed state plus the current row probabilities for Bullish, Neutral, and Bearish.
• The bottom bar shows a simple directional bias: P(Bull) - P(Bear).

P^2 and P^3 in this script are powers of the one-step probability. They are not full 2-step or 3-step Markov-chain forecasts produced by matrix multiplication.

• Threshold (%): Minimum absolute return needed to classify a bar as Bullish or Bearish.
• Timeframe: Higher timeframe used for the transition analysis.
• Lookback Window: Number of candles used to measure each return.
• Table Position: Screen location of the matrix.

• Diagonal cells show persistence. High values there mean a state often repeats.
• Off-diagonal cells show transitions. High values there mean a state often rotates into another one.
• A positive bottom-bar reading means Bullish transitions currently outweigh Bearish transitions from the latest confirmed state.
• A negative bottom-bar reading means Bearish transitions currently outweigh Bullish transitions from the latest confirmed state.

• The chart timeframe must be less than or equal to the selected analysis timeframe.
• The matrix is cumulative across all available history in the selected timeframe context.
• Changing timeframe, threshold, or lookback recompiles the script and rebuilds the tally from scratch.
• This is a state-transition study. It does not place trades or generate broker orders.

• Compare persistence vs reversal behavior across different symbols.
• Test whether a market spends more time trending or mean-reverting at a chosen timeframe.
• Check whether a recent state has historically led to bullish continuation, neutral drift, or bearish follow-through.