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 5.73% per annum.
- MDT price at the close of February 20, 2025 was $87.94 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 13.62% per annum.
- MDT 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 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: February 20, 2025
a = 4.1694
b = 0.0002
s = 0.0540
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0002) – 1
= 5.73%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0540) – 1
= 24.11%
September 21, 2022 calculations
Top border of price channel:
Exp(Y651)
= Exp(a + b × X651 + 2 × s)
= Exp(a + b × 943 + 2 × s)
= Exp(4.1694 + 0.0002 × 943 + 2 × 0.0540)
= Exp(4.4214)
= $83.21
Bottom border of price channel:
Exp(Y651)
= Exp(a + b × X651 – 2 × s)
= Exp(a + b × 943 – 2 × s)
= Exp(4.1694 + 0.0002 × 943 – 2 × 0.0540)
= Exp(4.2053)
= $67.04
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(4.1694 + 0.0002 × 1,826 + 2 × 0.0540)
= Exp(4.5562)
= $95.22
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(4.1694 + 0.0002 × 1,826 – 2 × 0.0540)
= Exp(4.3401)
= $76.72
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 5.73% per annum.
- MDT price at the close of February 20, 2025 was $87.94 and was inside the primary price channel.
Secondary Trend
Start date: September 26, 2023
End date: February 20, 2025
a = 3.8492
b = 0.0003
s = 0.0505
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0003) – 1
= 13.62%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0505) – 1
= 22.38%
September 26, 2023 calculations
Top border of price channel:
Exp(Y905)
= Exp(a + b × X905 + 2 × s)
= Exp(a + b × 1,313 + 2 × s)
= Exp(3.8492 + 0.0003 × 1,313 + 2 × 0.0505)
= Exp(4.4095)
= $82.23
Bottom border of price channel:
Exp(Y905)
= Exp(a + b × X905 – 2 × s)
= Exp(a + b × 1,313 – 2 × s)
= Exp(3.8492 + 0.0003 × 1,313 – 2 × 0.0505)
= Exp(4.2075)
= $67.19
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(3.8492 + 0.0003 × 1,826 + 2 × 0.0505)
= Exp(4.5889)
= $98.39
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.8492 + 0.0003 × 1,826 – 2 × 0.0505)
= Exp(4.3869)
= $80.39
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 13.62% per annum.
- MDT 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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