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 5.12% per annum.
- MDT price at the close of January 17, 2025 was $88.08 and was inside the primary price channel.
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 24.83% per annum.
- MDT price at the close of January 17, 2025 was higher than the top border of the secondary price channel by $2.34 (2.73%). This indicates a possible reversal in the secondary trend direction.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
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: January 17, 2025
a = 4.1848
b = 0.0001
s = 0.0535
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0001) – 1
= 5.12%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0535) – 1
= 23.88%
September 21, 2022 calculations
Top border of price channel:
Exp(Y673)
= Exp(a + b × X673 + 2 × s)
= Exp(a + b × 974 + 2 × s)
= Exp(4.1848 + 0.0001 × 974 + 2 × 0.0535)
= Exp(4.4250)
= $83.51
Bottom border of price channel:
Exp(Y673)
= Exp(a + b × X673 – 2 × s)
= Exp(a + b × 974 – 2 × s)
= Exp(4.1848 + 0.0001 × 974 – 2 × 0.0535)
= Exp(4.2109)
= $67.42
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(4.1848 + 0.0001 × 1,823 + 2 × 0.0535)
= Exp(4.5410)
= $93.79
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(4.1848 + 0.0001 × 1,823 – 2 × 0.0535)
= Exp(4.3269)
= $75.71
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 5.12% per annum.
- MDT price at the close of January 17, 2025 was $88.08 and was inside the primary price channel.
Secondary Trend
Start date: September 4, 2024
End date: January 17, 2025
a = 5.8254
b = -0.0008
s = 0.0257
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0008) – 1
= -24.83%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0257) – 1
= 10.82%
September 4, 2024 calculations
Top border of price channel:
Exp(Y1,163)
= Exp(a + b × X1,163 + 2 × s)
= Exp(a + b × 1,688 + 2 × s)
= Exp(5.8254 + -0.0008 × 1,688 + 2 × 0.0257)
= Exp(4.5569)
= $95.28
Bottom border of price channel:
Exp(Y1,163)
= Exp(a + b × X1,163 – 2 × s)
= Exp(a + b × 1,688 – 2 × s)
= Exp(5.8254 + -0.0008 × 1,688 – 2 × 0.0257)
= Exp(4.4541)
= $85.98
January 17, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,823 + 2 × s)
= Exp(5.8254 + -0.0008 × 1,823 + 2 × 0.0257)
= Exp(4.4513)
= $85.74
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,823 – 2 × s)
= Exp(5.8254 + -0.0008 × 1,823 – 2 × 0.0257)
= Exp(4.3485)
= $77.36
Description
- The secondary trend is decreasing.
- The decline rate of the secondary trend is 24.83% per annum.
- MDT price at the close of January 17, 2025 was higher than the top border of the secondary price channel by $2.34 (2.73%). This indicates a possible reversal in the secondary trend direction.
- 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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