QuanTAlib/lib/core/midprice/Midprice.md

MIDPRICE: Midpoint Price over Period

The midpoint of highest high and lowest low over a period anchors price to its range center.

Property	Value
Category	Core
Inputs	OHLCV bar (TBar)
Parameters	period
Outputs	Single series (Midprice)
Output range	Varies (see docs)
Warmup	period bars
PineScript	midprice.pine

• MIDPRICE computes the center of a rolling price channel by averaging the highest High and lowest Low over the past N bars: $(\text{Highest}(H, N)...
• Similar: MidPoint, TypPrice | Trading note: (High+Low)/2; common price proxy for indicators avoiding close bias.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

MIDPRICE computes the center of a rolling price channel by averaging the highest High and lowest Low over the past N bars: (\text{Highest}(H, N) + \text{Lowest}(L, N)) \times 0.5. Unlike the stateless price transforms (AVGPRICE, MEDPRICE, TYPPRICE, WCLPRICE) that operate on a single bar, MIDPRICE maintains a lookback window and produces a rolling estimate of the price range's midpoint. This makes it a simplified channel center line, equivalent to the midpoint of a Donchian Channel. The calculation uses two internal RingBuffers for O(N) max/min computation per bar. TA-Lib compatible via TA_MIDPRICE.

Historical Context

MIDPRICE is the simplest possible channel-based price reference, conceptually dating back to Richard Donchian's channel breakout work in the 1960s. Where Donchian Channels plot the full upper/lower envelope, MIDPRICE extracts only the midline. The TA-Lib function TA_MIDPRICE takes separate High and Low arrays and a period parameter, which distinguishes it from TA_MIDPOINT (which operates on a single series).

The distinction between MIDPRICE and MIDPOINT matters:

• MIDPOINT: (\text{Highest}(V, N) + \text{Lowest}(V, N)) \times 0.5 on a single value series
• MIDPRICE: (\text{Highest}(H, N) + \text{Lowest}(L, N)) \times 0.5 on separate High/Low channels

MIDPRICE always produces a wider (or equal) range because the highest High is at least as large as the highest Close, and the lowest Low is at most as small as the lowest Close. This makes MIDPRICE a more conservative channel center, reflecting the full extent of price exploration rather than just settlement levels.

Architecture & Physics

1. Core Formula

\text{MidPrice}_t = \left(\max_{i=0}^{N-1} H_{t-i} + \min_{i=0}^{N-1} L_{t-i}\right) \times 0.5

2. Rolling Window Implementation

Two independent RingBuffer instances maintain the last N High and Low values:

• _highBuffer: Stores High values; Max() returns the rolling maximum
• _lowBuffer: Stores Low values; Min() returns the rolling minimum

The RingBuffer.Max() and RingBuffer.Min() operations scan the buffer linearly, making each Update call O(N). This was a deliberate design choice to avoid the cross-project dependency that composing Highest/Lowest indicator instances from lib/numerics/ would introduce. The core library must remain self-contained for Quantower builds.

3. State Management

• RingBuffer snapshots: isNew=true captures buffer state via Snapshot(); isNew=false restores via Restore() for bar correction.
• Last-valid substitution: Non-finite High or Low values are replaced with the last known finite value.
• Warmup: IsHot becomes true when the buffer reaches period elements.

4. Complexity

O(N) per bar where N is the period, due to linear scan for max/min. For typical periods (5-20), this is negligible. Always-hot after N bars.

Mathematical Foundation

Parameters

Parameter	Description	Default	Constraint
period	Lookback window for rolling max/min (N)	(required)	\geq 1

MIDPRICE vs Related Indicators

Indicator	Formula	Input	State
MIDPRICE	(\max(H,N) + \min(L,N)) \times 0.5	TBar (H/L channels)	Rolling window
MIDPOINT	(\max(V,N) + \min(V,N)) \times 0.5	Single series	Rolling window
MEDPRICE	(H + L) \times 0.5	TBar (single bar)	Stateless
Donchian Mid	Same as MIDPRICE	TBar (H/L channels)	Rolling window

Output Interpretation

Context	Meaning
Price > MIDPRICE	Trading in the upper half of the $N$-bar channel
Price < MIDPRICE	Trading in the lower half of the $N$-bar channel
MIDPRICE rising	Channel shifting upward (uptrend)
MIDPRICE flat	Range-bound market; channel stable
MIDPRICE converging with price	Trend exhaustion; approaching channel center

Performance Profile

Operation Count (Streaming Mode)

Operation	Count	Cost (cycles)	Subtotal
RingBuffer.Add (high)	1	~3	3
RingBuffer.Add (low)	1	~3	3
RingBuffer.Max() scan	N	~N	N
RingBuffer.Min() scan	N	~N	N
ADD (max+min)	1	1	1
MUL (× 0.5)	1	3	3
Total (hot)	$2N+4$		~2N + 10 cycles

For period=14: approximately 38 cycles per bar.

Batch Mode (SIMD Analysis)

Aspect	Assessment
SIMD vectorizable	Partial: max/min scans are sequential per window; final midpoint is vectorizable
Optimal strategy	Monotonic deque for O(1) amortized max/min (not yet implemented)
Memory	O(N): two RingBuffers of size N
Throughput	Dominated by max/min scans; ~5x slower than stateless transforms at period=14

Potential Optimization

A monotonic deque (sliding window max/min) would reduce per-bar cost from O(N) to O(1) amortized. This is a known optimization path stored for future implementation when profiling shows MIDPRICE as a bottleneck in production pipelines.

Resources

• TA-Lib TA_MIDPRICE function reference.
• Donchian, R. "High Finance in Copper." Financial Analysts Journal, 1960. (Origin of channel-based price analysis)
• Achelis, S.B. Technical Analysis from A to Z. McGraw-Hill, 2000.