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 66.90% per annum.
- MPC price at the close of May 7, 2024 was $180.92 and was lower than the bottom border of the primary price channel by $11.51 (5.98%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 49.08% per annum.
- MPC price at the close of May 7, 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 MPC 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: March 25, 2020
End date: April 24, 2023
a = 2.9105
b = 0.0014
s = 0.1067
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0014) – 1
= 66.90%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.1067) – 1
= 53.24%
March 25, 2020 calculations
Top border of price channel:
Exp(Y222)
= Exp(a + b × X222 + 2 × s)
= Exp(a + b × 322 + 2 × s)
= Exp(2.9105 + 0.0014 × 322 + 2 × 0.1067)
= Exp(3.5758)
= $35.72
Bottom border of price channel:
Exp(Y222)
= Exp(a + b × X222 – 2 × s)
= Exp(a + b × 322 – 2 × s)
= Exp(2.9105 + 0.0014 × 322 – 2 × 0.1067)
= Exp(3.1490)
= $23.31
April 24, 2023 calculations
Top border of price channel:
Exp(Y997)
= Exp(a + b × X997 + 2 × s)
= Exp(a + b × 1,447 + 2 × s)
= Exp(2.9105 + 0.0014 × 1,447 + 2 × 0.1067)
= Exp(5.1547)
= $173.24
Bottom border of price channel:
Exp(Y997)
= Exp(a + b × X997 – 2 × s)
= Exp(a + b × 1,447 – 2 × s)
= Exp(2.9105 + 0.0014 × 1,447 – 2 × 0.1067)
= Exp(4.7279)
= $113.05
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 66.90% per annum.
- MPC price at the close of May 7, 2024 was $180.92 and was lower than the bottom border of the primary price channel by $11.51 (5.98%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: February 3, 2021
End date: March 14, 2024
a = 3.2300
b = 0.0011
s = 0.0839
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0011) – 1
= 49.08%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0839) – 1
= 39.86%
February 3, 2021 calculations
Top border of price channel:
Exp(Y439)
= Exp(a + b × X439 + 2 × s)
= Exp(a + b × 637 + 2 × s)
= Exp(3.2300 + 0.0011 × 637 + 2 × 0.0839)
= Exp(4.0947)
= $60.02
Bottom border of price channel:
Exp(Y439)
= Exp(a + b × X439 – 2 × s)
= Exp(a + b × 637 – 2 × s)
= Exp(3.2300 + 0.0011 × 637 – 2 × 0.0839)
= Exp(3.7592)
= $42.92
March 14, 2024 calculations
Top border of price channel:
Exp(Y1,221)
= Exp(a + b × X1,221 + 2 × s)
= Exp(a + b × 1,772 + 2 × s)
= Exp(3.2300 + 0.0011 × 1,772 + 2 × 0.0839)
= Exp(5.3364)
= $207.77
Bottom border of price channel:
Exp(Y1,221)
= Exp(a + b × X1,221 – 2 × s)
= Exp(a + b × 1,772 – 2 × s)
= Exp(3.2300 + 0.0011 × 1,772 – 2 × 0.0839)
= Exp(5.0010)
= $148.56
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 49.08% per annum.
- MPC price at the close of May 7, 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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