Time-Series Operators¶
Operators that compute values over time for each asset independently.
Basic Operations¶
lag(x, n)¶
Shift values back by n periods.
Text Only
signal example:
previous_price = lag(prices, 1) // Yesterday's price
week_ago_price = lag(prices, 5) // 5 days ago
month_ago_price = lag(prices, 21) // ~1 month ago
emit previous_price
ret(x, n)¶
Compute n-period return: (x - lag(x, n)) / lag(x, n)
Text Only
signal example:
daily_return = ret(prices, 1) // 1-day return
weekly_return = ret(prices, 5) // 5-day return
monthly_return = ret(prices, 21) // ~1-month return
annual_return = ret(prices, 252) // ~1-year return
emit monthly_return
delta(x, n)¶
Compute n-period difference: x - lag(x, n)
Text Only
signal example:
price_change = delta(prices, 1) // $ change
volume_change = delta(volume, 5) // Volume change
emit price_change
Rolling Statistics¶
rolling_mean(x, n)¶
Rolling mean (moving average).
Text Only
signal example:
sma_20 = rolling_mean(prices, 20) // 20-day SMA
sma_50 = rolling_mean(prices, 50) // 50-day SMA
avg_volume = rolling_mean(volume, 20)
emit sma_20
rolling_std(x, n)¶
Rolling standard deviation.
Text Only
signal example:
daily_ret = ret(prices, 1)
volatility = rolling_std(daily_ret, 20) // 20-day vol
annualized_vol = volatility * sqrt(252)
emit volatility
rolling_sum(x, n)¶
Rolling sum.
Text Only
signal example:
volume_20d = rolling_sum(volume, 20)
cum_return_5d = rolling_sum(ret(prices, 1), 5)
emit volume_20d
rolling_min(x, n)¶
Rolling minimum.
Text Only
signal example:
low_20d = rolling_min(prices, 20)
support = rolling_min(prices, 52 * 5) // 52-week low
emit low_20d
rolling_max(x, n)¶
Rolling maximum.
Text Only
signal example:
high_20d = rolling_max(prices, 20)
resistance = rolling_max(prices, 52 * 5) // 52-week high
emit high_20d
rolling_corr(x, y, n)¶
Rolling correlation between two series.
Text Only
signal example:
// Correlation with market
market_corr = rolling_corr(stock_returns, market_returns, 60)
// Pairs correlation
pair_corr = rolling_corr(ret(stock_a, 1), ret(stock_b, 1), 20)
emit market_corr
Exponential Moving Average¶
ema(x, span)¶
Exponential moving average.
Text Only
signal example:
ema_10 = ema(prices, 10)
ema_20 = ema(prices, 20)
ema_50 = ema(prices, 50)
// EMA crossover signal
crossover = ema_10 - ema_50
emit crossover
EMA formula: \(\alpha = 2 / (span + 1)\)
decay_linear(x, n)¶
Linear decay weighted average.
Recent values have higher weights:
Text Only
signal example:
// Recent days weighted more heavily
weighted_return = decay_linear(ret(prices, 1), 20)
emit weighted_return
Advanced Time-Series¶
ts_argmax(x, n)¶
Index of maximum value in window (days since max).
Text Only
signal example:
// Days since 20-day high
days_since_high = ts_argmax(prices, 20)
emit days_since_high
ts_argmin(x, n)¶
Index of minimum value in window (days since min).
Text Only
signal example:
// Days since 20-day low
days_since_low = ts_argmin(prices, 20)
emit days_since_low
ts_rank(x, n)¶
Time-series rank (rank within asset's own history).
Text Only
signal example:
// How current price ranks vs last 20 days
ts_rank_20 = ts_rank(prices, 20)
emit ts_rank_20
ts_skew(x, n)¶
Rolling skewness.
ts_kurt(x, n)¶
Rolling kurtosis.
Text Only
signal example:
return_kurt = ts_kurt(ret(prices, 1), 60)
// High kurtosis = fat tails
emit return_kurt
ts_product(x, n)¶
Rolling product.
Text Only
signal example:
// Cumulative return over window
growth_factors = 1 + ret(prices, 1)
cum_return = ts_product(growth_factors, 20) - 1
emit cum_return
ts_zscore(x, n)¶
Time-series z-score (normalize within asset's history).
Text Only
signal example:
// Current price relative to own history
price_zscore = ts_zscore(prices, 252)
// Positive = above historical mean
emit price_zscore
Common Patterns¶
Momentum¶
Text Only
signal momentum:
// 12-month return minus 1-month return
r12 = ret(prices, 252)
r1 = ret(prices, 21)
mom = r12 - r1
emit zscore(mom)
Moving Average Crossover¶
Text Only
signal ma_crossover:
fast = ema(prices, 10)
slow = ema(prices, 50)
crossover = (fast - slow) / slow
emit zscore(crossover)
Volatility¶
Text Only
signal volatility:
daily_ret = ret(prices, 1)
vol_20 = rolling_std(daily_ret, 20)
vol_60 = rolling_std(daily_ret, 60)
// Ratio of short to long vol
vol_ratio = vol_20 / vol_60
emit zscore(vol_ratio)
Bollinger Bands¶
Text Only
signal bollinger:
ma = rolling_mean(prices, 20)
std = rolling_std(prices, 20)
z = (prices - ma) / std
emit z // Position within bands
Relative Strength¶
Text Only
signal relative_strength:
// Price relative to 52-week range
high_52 = rolling_max(prices, 252)
low_52 = rolling_min(prices, 252)
rs = (prices - low_52) / (high_52 - low_52)
emit rs
Channel Breakout¶
Text Only
signal breakout:
high_20 = rolling_max(prices, 20)
low_20 = rolling_min(prices, 20)
mid = (high_20 + low_20) / 2
// Position in channel (0 = bottom, 1 = top)
position = (prices - low_20) / (high_20 - low_20)
emit position
Warm-up Period¶
Rolling operators require a warm-up period:
Text Only
// rolling_mean(x, 20) produces NaN for first 19 rows
// Because there aren't enough observations yet
Handle with fill_nan if needed:
Type Behavior¶
All time-series operators:
- Input: Panel (dates × assets)
- Output: Panel (same shape)
- Operate on each asset independently
Next Steps¶
- Cross-Sectional - Across-asset operators
- Technical - Technical indicators
- Signal Section - Using in signals