Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 14.77% per annum.
- DIS price at the close of February 20, 2025 was $110.55 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 76.35% per annum.
- DIS price at the close of February 20, 2025 was inside the secondary price channel.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of DIS price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: May 11, 2023
End date: February 20, 2025
a = 4.0004
b = 0.0004
s = 0.0894
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 14.77%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0894) – 1
= 43.00%
May 11, 2023 calculations
Top border of price channel:
Exp(Y811)
= Exp(a + b × X811 + 2 × s)
= Exp(a + b × 1,175 + 2 × s)
= Exp(4.0004 + 0.0004 × 1,175 + 2 × 0.0894)
= Exp(4.6226)
= $101.76
Bottom border of price channel:
Exp(Y811)
= Exp(a + b × X811 – 2 × s)
= Exp(a + b × 1,175 – 2 × s)
= Exp(4.0004 + 0.0004 × 1,175 – 2 × 0.0894)
= Exp(4.2649)
= $71.16
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(4.0004 + 0.0004 × 1,826 + 2 × 0.0894)
= Exp(4.8682)
= $130.09
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.0004 + 0.0004 × 1,826 – 2 × 0.0894)
= Exp(4.5106)
= $90.97
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 14.77% per annum.
- DIS price at the close of February 20, 2025 was $110.55 and was inside the primary price channel.
Secondary Trend
Start date: August 2, 2024
End date: February 20, 2025
a = 1.9372
b = 0.0016
s = 0.0482
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0016) – 1
= 76.35%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0482) – 1
= 21.28%
August 2, 2024 calculations
Top border of price channel:
Exp(Y1,119)
= Exp(a + b × X1,119 + 2 × s)
= Exp(a + b × 1,624 + 2 × s)
= Exp(1.9372 + 0.0016 × 1,624 + 2 × 0.0482)
= Exp(4.5578)
= $95.37
Bottom border of price channel:
Exp(Y1,119)
= Exp(a + b × X1,119 – 2 × s)
= Exp(a + b × 1,624 – 2 × s)
= Exp(1.9372 + 0.0016 × 1,624 – 2 × 0.0482)
= Exp(4.3649)
= $78.64
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(1.9372 + 0.0016 × 1,826 + 2 × 0.0482)
= Exp(4.8718)
= $130.55
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(1.9372 + 0.0016 × 1,826 – 2 × 0.0482)
= Exp(4.6788)
= $107.64
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 76.35% per annum.
- DIS price at the close of February 20, 2025 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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