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 6.38% per annum.
- MDT price at the close of March 28, 2025 was $87.63 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 14.25% per annum.
- MDT price at the close of March 28, 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 MDT 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: September 21, 2022
End date: March 28, 2025
a = 4.1469
b = 0.0002
s = 0.0544
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 6.38%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0544) – 1
= 24.33%
September 21, 2022 calculations
Top border of price channel:
Exp(Y625)
= Exp(a + b × X625 + 2 × s)
= Exp(a + b × 905 + 2 × s)
= Exp(4.1469 + 0.0002 × 905 + 2 × 0.0544)
= Exp(4.4092)
= $82.21
Bottom border of price channel:
Exp(Y625)
= Exp(a + b × X625 – 2 × s)
= Exp(a + b × 905 – 2 × s)
= Exp(4.1469 + 0.0002 × 905 – 2 × 0.0544)
= Exp(4.1914)
= $66.12
March 28, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(4.1469 + 0.0002 × 1,824 + 2 × 0.0544)
= Exp(4.5650)
= $96.07
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.1469 + 0.0002 × 1,824 – 2 × 0.0544)
= Exp(4.3472)
= $77.26
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 6.38% per annum.
- MDT price at the close of March 28, 2025 was $87.63 and was inside the primary price channel.
Secondary Trend
Start date: September 26, 2023
End date: March 28, 2025
a = 3.8327
b = 0.0004
s = 0.0493
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0004) – 1
= 14.25%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0493) – 1
= 21.81%
September 26, 2023 calculations
Top border of price channel:
Exp(Y879)
= Exp(a + b × X879 + 2 × s)
= Exp(a + b × 1,275 + 2 × s)
= Exp(3.8327 + 0.0004 × 1,275 + 2 × 0.0493)
= Exp(4.3965)
= $81.17
Bottom border of price channel:
Exp(Y879)
= Exp(a + b × X879 – 2 × s)
= Exp(a + b × 1,275 – 2 × s)
= Exp(3.8327 + 0.0004 × 1,275 – 2 × 0.0493)
= Exp(4.1993)
= $66.64
March 28, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(3.8327 + 0.0004 × 1,824 + 2 × 0.0493)
= Exp(4.5968)
= $99.17
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(3.8327 + 0.0004 × 1,824 – 2 × 0.0493)
= Exp(4.3996)
= $81.42
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 14.25% per annum.
- MDT price at the close of March 28, 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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