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 43.57% per annum.
- MU price at the close of April 26, 2024 was $114.84 and was higher than the top border of the primary price channel by $14.21 (14.12%).
- The secondary trend is increasing.
- The growth rate of the secondary trend is 164.09% per annum.
- MU price at the close of April 26, 2024 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 MU 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 13, 2022
End date: March 20, 2024
a = 2.6861
b = 0.0010
s = 0.0590
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0010) – 1
= 43.57%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0590) – 1
= 26.62%
September 13, 2022 calculations
Top border of price channel:
Exp(Y851)
= Exp(a + b × X851 + 2 × s)
= Exp(a + b × 1,233 + 2 × s)
= Exp(2.6861 + 0.0010 × 1,233 + 2 × 0.0590)
= Exp(4.0259)
= $56.03
Bottom border of price channel:
Exp(Y851)
= Exp(a + b × X851 – 2 × s)
= Exp(a + b × 1,233 – 2 × s)
= Exp(2.6861 + 0.0010 × 1,233 – 2 × 0.0590)
= Exp(3.7898)
= $44.25
March 20, 2024 calculations
Top border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 + 2 × s)
= Exp(a + b × 1,787 + 2 × s)
= Exp(2.6861 + 0.0010 × 1,787 + 2 × 0.0590)
= Exp(4.5748)
= $97.01
Bottom border of price channel:
Exp(Y1,232)
= Exp(a + b × X1,232 – 2 × s)
= Exp(a + b × 1,787 – 2 × s)
= Exp(2.6861 + 0.0010 × 1,787 – 2 × 0.0590)
= Exp(4.3388)
= $76.61
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 43.57% per annum.
- MU price at the close of April 26, 2024 was $114.84 and was higher than the top border of the primary price channel by $14.21 (14.12%).
Secondary Trend
Start date: September 21, 2023
End date: April 26, 2024
a = -0.1227
b = 0.0027
s = 0.0682
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0027) – 1
= 164.09%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0682) – 1
= 31.37%
September 21, 2023 calculations
Top border of price channel:
Exp(Y1,108)
= Exp(a + b × X1,108 + 2 × s)
= Exp(a + b × 1,606 + 2 × s)
= Exp(-0.1227 + 0.0027 × 1,606 + 2 × 0.0682)
= Exp(4.2866)
= $72.72
Bottom border of price channel:
Exp(Y1,108)
= Exp(a + b × X1,108 – 2 × s)
= Exp(a + b × 1,606 – 2 × s)
= Exp(-0.1227 + 0.0027 × 1,606 – 2 × 0.0682)
= Exp(4.0137)
= $55.35
April 26, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(-0.1227 + 0.0027 × 1,824 + 2 × 0.0682)
= Exp(4.8666)
= $129.88
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(-0.1227 + 0.0027 × 1,824 – 2 × 0.0682)
= Exp(4.5937)
= $98.86
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 164.09% per annum.
- MU price at the close of April 26, 2024 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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